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Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Autore Hughes Bruce
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2000
Descrizione fisica 1 online resource (113 p.)
Disciplina 510 s
514/.3
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite-dimensional manifolds
K-theory
Soggetto genere / forma Electronic books.
ISBN 1-4704-0282-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction and Statement of Results""; ""1.1. Introduction""; ""1.2. Statement of Results""; ""Chapter 2. Moduli Spaces of Manifolds and Maps""; ""2.1. The Simplcial Set of Manifolds""; ""2.2. The Simplcial Set of Manifold Approximate Fibrations""; ""2.3. The Simplcial Set of Manifold Bands""; ""2.4. The Forget Control Map""; ""Chapter 3. Wrapping�up and Unwrapping as Simplcial Maps""; ""3.1. Unwrapping""; ""3.2. Wrapping Up""; ""3.3. Definition of w""; ""3.4. Classifying Space Interpretation""; ""3.5. Independence of Covering Isotopy""
""Chapter 4. Relaxation as a Simplcial Map""""Chapter 5. The Whitehead Spaces""; ""5.1. The Controlled Whitehead Space""; ""5.2. Abelian Monoid�like Structures""; ""5.3. The Various SimpHcial Maps""; ""5.4. The Forget Control Map""; ""5.5. The Unwrapping Map""; ""5.6. The Wrapping Up Map""; ""5.7. Classifying Space Interpretation""; ""5.8. Delooping the Whitehead Space""; ""5.9. The Relaxation Map""; ""5.10. The Boundedness Condition on the Infinite Cyclic Cover""; ""5.11. Bounded Whitehead and Pseudoisotopy Spaces""; ""Chapter 6. Torsion and a Higher Sum Theorem""
""9.2. Description of Finite Structures on Mapping Tori""""9.3. Definition of an Embedding M â?? T(w)""; ""9.4. Definition of the Relaxation""; ""9.5. Splittings""; ""9.6. Splitting of T"", Second Splitting of T(w)""; ""9.7. Completion of the Proof""; ""Chapter 10. Comparison with the Lower Algebraic Nil Groups""; ""10.1. Preliminaries on the Algebraic Lower Nilâ€?Groups""; ""10.2. The Definition of the Homomorphism between Algebraic and Geometric Nilâ€?groups""; ""10.3. Delooping of Nilâ€?spaces""; ""Appendix A. Controlled Homotopies on Mapping Tori""; ""Bibliography""
Record Nr. UNINA-9910480869703321
Hughes Bruce  
Providence, Rhode Island : , : American Mathematical Society, , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Autore Hughes Bruce
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2000
Descrizione fisica 1 online resource (113 p.)
Disciplina 510 s
514/.3
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite-dimensional manifolds
K-theory
ISBN 1-4704-0282-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction and Statement of Results""; ""1.1. Introduction""; ""1.2. Statement of Results""; ""Chapter 2. Moduli Spaces of Manifolds and Maps""; ""2.1. The Simplcial Set of Manifolds""; ""2.2. The Simplcial Set of Manifold Approximate Fibrations""; ""2.3. The Simplcial Set of Manifold Bands""; ""2.4. The Forget Control Map""; ""Chapter 3. Wrapping�up and Unwrapping as Simplcial Maps""; ""3.1. Unwrapping""; ""3.2. Wrapping Up""; ""3.3. Definition of w""; ""3.4. Classifying Space Interpretation""; ""3.5. Independence of Covering Isotopy""
""Chapter 4. Relaxation as a Simplcial Map""""Chapter 5. The Whitehead Spaces""; ""5.1. The Controlled Whitehead Space""; ""5.2. Abelian Monoid�like Structures""; ""5.3. The Various SimpHcial Maps""; ""5.4. The Forget Control Map""; ""5.5. The Unwrapping Map""; ""5.6. The Wrapping Up Map""; ""5.7. Classifying Space Interpretation""; ""5.8. Delooping the Whitehead Space""; ""5.9. The Relaxation Map""; ""5.10. The Boundedness Condition on the Infinite Cyclic Cover""; ""5.11. Bounded Whitehead and Pseudoisotopy Spaces""; ""Chapter 6. Torsion and a Higher Sum Theorem""
""9.2. Description of Finite Structures on Mapping Tori""""9.3. Definition of an Embedding M â?? T(w)""; ""9.4. Definition of the Relaxation""; ""9.5. Splittings""; ""9.6. Splitting of T"", Second Splitting of T(w)""; ""9.7. Completion of the Proof""; ""Chapter 10. Comparison with the Lower Algebraic Nil Groups""; ""10.1. Preliminaries on the Algebraic Lower Nilâ€?Groups""; ""10.2. The Definition of the Homomorphism between Algebraic and Geometric Nilâ€?groups""; ""10.3. Delooping of Nilâ€?spaces""; ""Appendix A. Controlled Homotopies on Mapping Tori""; ""Bibliography""
Record Nr. UNINA-9910788840803321
Hughes Bruce  
Providence, Rhode Island : , : American Mathematical Society, , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Control and relaxation over the circle / / Bruce Hughes, Stratos Prassidis
Autore Hughes Bruce
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2000
Descrizione fisica 1 online resource (113 p.)
Disciplina 510 s
514/.3
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite-dimensional manifolds
K-theory
ISBN 1-4704-0282-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Chapter 1. Introduction and Statement of Results""; ""1.1. Introduction""; ""1.2. Statement of Results""; ""Chapter 2. Moduli Spaces of Manifolds and Maps""; ""2.1. The Simplcial Set of Manifolds""; ""2.2. The Simplcial Set of Manifold Approximate Fibrations""; ""2.3. The Simplcial Set of Manifold Bands""; ""2.4. The Forget Control Map""; ""Chapter 3. Wrapping�up and Unwrapping as Simplcial Maps""; ""3.1. Unwrapping""; ""3.2. Wrapping Up""; ""3.3. Definition of w""; ""3.4. Classifying Space Interpretation""; ""3.5. Independence of Covering Isotopy""
""Chapter 4. Relaxation as a Simplcial Map""""Chapter 5. The Whitehead Spaces""; ""5.1. The Controlled Whitehead Space""; ""5.2. Abelian Monoid�like Structures""; ""5.3. The Various SimpHcial Maps""; ""5.4. The Forget Control Map""; ""5.5. The Unwrapping Map""; ""5.6. The Wrapping Up Map""; ""5.7. Classifying Space Interpretation""; ""5.8. Delooping the Whitehead Space""; ""5.9. The Relaxation Map""; ""5.10. The Boundedness Condition on the Infinite Cyclic Cover""; ""5.11. Bounded Whitehead and Pseudoisotopy Spaces""; ""Chapter 6. Torsion and a Higher Sum Theorem""
""9.2. Description of Finite Structures on Mapping Tori""""9.3. Definition of an Embedding M â?? T(w)""; ""9.4. Definition of the Relaxation""; ""9.5. Splittings""; ""9.6. Splitting of T"", Second Splitting of T(w)""; ""9.7. Completion of the Proof""; ""Chapter 10. Comparison with the Lower Algebraic Nil Groups""; ""10.1. Preliminaries on the Algebraic Lower Nilâ€?Groups""; ""10.2. The Definition of the Homomorphism between Algebraic and Geometric Nilâ€?groups""; ""10.3. Delooping of Nilâ€?spaces""; ""Appendix A. Controlled Homotopies on Mapping Tori""; ""Bibliography""
Record Nr. UNINA-9910808070103321
Hughes Bruce  
Providence, Rhode Island : , : American Mathematical Society, , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Controlled simple homotopy theory and applications / / T. A. Chapman
Controlled simple homotopy theory and applications / / T. A. Chapman
Autore Chapman T. A (Thomas A.), <1940->
Edizione [1st ed. 1983.]
Pubbl/distr/stampa Heidelberg : , : Springer-Verlag, , [1983]
Descrizione fisica 1 online resource (III, 94 p.)
Disciplina 514.24
Collana Lecture notes in mathematics (Springer-Verlag)
Soggetto topico Homotopy theory
Infinite-dimensional manifolds
Topology
ISBN 3-540-40973-4
Classificazione 57Q10
57R80
57R67
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Applications -- Definitions and notation -- Construction of Wh(y)? -- Functorial properties -- Controlled whitehead torsion -- Construction of K0(Y)? -- Controlled finiteness obstruction -- Further properties of the controlled finiteness obstruction -- The splitting homomorphism -- The splitting sequence -- The realization theorem -- Calculations -- The Controlled Boundary Theorem -- The Controlled s-Cobordism Theorem.
Record Nr. UNISA-996466595103316
Chapman T. A (Thomas A.), <1940->  
Heidelberg : , : Springer-Verlag, , [1983]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Autore Gangbo Wilfrid
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2010
Descrizione fisica 1 online resource (77 p.)
Disciplina 515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Differential forms
Hamiltonian systems
Infinite-dimensional manifolds
Soggetto genere / forma Electronic books.
ISBN 1-4704-0610-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles""
""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M""
""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography""
Record Nr. UNINA-9910481052303321
Gangbo Wilfrid  
Providence, Rhode Island : , : American Mathematical Society, , 2010
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Autore Gangbo Wilfrid
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2010
Descrizione fisica 1 online resource (77 p.)
Disciplina 515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Differential forms
Hamiltonian systems
Infinite-dimensional manifolds
ISBN 1-4704-0610-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles""
""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M""
""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography""
Record Nr. UNINA-9910788866103321
Gangbo Wilfrid  
Providence, Rhode Island : , : American Mathematical Society, , 2010
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Autore Gangbo Wilfrid
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2010
Descrizione fisica 1 online resource (77 p.)
Disciplina 515/.39
Collana Memoirs of the American Mathematical Society
Soggetto topico Differential forms
Hamiltonian systems
Infinite-dimensional manifolds
ISBN 1-4704-0610-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles""
""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M""
""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography""
Record Nr. UNINA-9910827648403321
Gangbo Wilfrid  
Providence, Rhode Island : , : American Mathematical Society, , 2010
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Autore Bertram Wolfgang <1965->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2008]
Descrizione fisica 1 online resource (218 p.)
Disciplina 510 s
512/.482
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite dimensional Lie algebras
Infinite-dimensional manifolds
Symmetric spaces
Geometry, Differential
Soggetto genere / forma Electronic books.
ISBN 1-4704-0506-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""I. Basic notions""; ""1. Differential calculus""; ""2. Manifolds""; ""3. Tangent bundle and general fiber bundles""; ""4. The Lie bracket of vector fields""; ""5. Lie groups and symmetric spaces: basic facts""; ""II. Interpretation of tangent objects via scalar extensions""; ""6. Scalar extensions. I: Tangent functor and dual numbers""; ""7. Scalar extensions. II: Higher order tangent functors""; ""8. Scalar extensions. Ill: Jet functor and truncated polynomial rings""; ""III. Second order differential geometry""
""9. The structure of the tangent bundle of a vector bundle""""10. Linear connections. I: Linear structures on bilinear bundles""; ""11. Linear connections. II: Sprays""; ""12. Linear connections. Ill: Covariant derivative""; ""13. Natural operations. I: Exterior derivative of a one-form""; ""14. Natural operations. II: The Lie bracket revisited""; ""IV. Third and higher order differential geometry""; ""15. The structure of T[sup(k)]F: Multilinear bundles""; ""16. The structure of T[sup(k)]F: Multilinear connections""; ""17. Construction of multilinear connections""; ""18. Curvature""
""19. Linear structures on jet bundles""""20. Shifts and symmetrization""; ""21. Remarks on differential operators and symbols""; ""22. The exterior derivative""; ""V. Lie Theory""; ""23. The three canonical connections of a Lie group""; ""24. The structure of higher order tangent groups""; ""25. Exponential map and Campbell-Hausdorff formula""; ""26. The canonical connection of a symmetric space""; ""27. The higher order tangent structure of symmetric spaces""; ""VI.Diffeomorphism Groups and the exponential jet""; ""28. Group structure on the space of sections of T[sup(k)]M""
""29. The exponential jet for vector fields""""30. The exponential jet of a symmetric space""; ""31. Remarks on the exponential jet of a general connection""; ""32. From germs to jets and from jets to germs""; ""Appendix L. Limitations""; ""Appendix G. Generalizations""; ""Appendix: Multilinear Geometry""; ""BA. Bilinear algebra""; ""MA. Multilinear algebra""; ""SA. Symmetric and shift invariant multilinear algebra""; ""PG. Polynomial groups""; ""References""
Record Nr. UNINA-9910480857603321
Bertram Wolfgang <1965->  
Providence, Rhode Island : , : American Mathematical Society, , [2008]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Autore Bertram Wolfgang <1965->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2008]
Descrizione fisica 1 online resource (218 p.)
Disciplina 510 s
512/.482
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite dimensional Lie algebras
Infinite-dimensional manifolds
Symmetric spaces
Geometry, Differential
ISBN 1-4704-0506-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""I. Basic notions""; ""1. Differential calculus""; ""2. Manifolds""; ""3. Tangent bundle and general fiber bundles""; ""4. The Lie bracket of vector fields""; ""5. Lie groups and symmetric spaces: basic facts""; ""II. Interpretation of tangent objects via scalar extensions""; ""6. Scalar extensions. I: Tangent functor and dual numbers""; ""7. Scalar extensions. II: Higher order tangent functors""; ""8. Scalar extensions. Ill: Jet functor and truncated polynomial rings""; ""III. Second order differential geometry""
""9. The structure of the tangent bundle of a vector bundle""""10. Linear connections. I: Linear structures on bilinear bundles""; ""11. Linear connections. II: Sprays""; ""12. Linear connections. Ill: Covariant derivative""; ""13. Natural operations. I: Exterior derivative of a one-form""; ""14. Natural operations. II: The Lie bracket revisited""; ""IV. Third and higher order differential geometry""; ""15. The structure of T[sup(k)]F: Multilinear bundles""; ""16. The structure of T[sup(k)]F: Multilinear connections""; ""17. Construction of multilinear connections""; ""18. Curvature""
""19. Linear structures on jet bundles""""20. Shifts and symmetrization""; ""21. Remarks on differential operators and symbols""; ""22. The exterior derivative""; ""V. Lie Theory""; ""23. The three canonical connections of a Lie group""; ""24. The structure of higher order tangent groups""; ""25. Exponential map and Campbell-Hausdorff formula""; ""26. The canonical connection of a symmetric space""; ""27. The higher order tangent structure of symmetric spaces""; ""VI.Diffeomorphism Groups and the exponential jet""; ""28. Group structure on the space of sections of T[sup(k)]M""
""29. The exponential jet for vector fields""""30. The exponential jet of a symmetric space""; ""31. Remarks on the exponential jet of a general connection""; ""32. From germs to jets and from jets to germs""; ""Appendix L. Limitations""; ""Appendix G. Generalizations""; ""Appendix: Multilinear Geometry""; ""BA. Bilinear algebra""; ""MA. Multilinear algebra""; ""SA. Symmetric and shift invariant multilinear algebra""; ""PG. Polynomial groups""; ""References""
Record Nr. UNINA-9910788851903321
Bertram Wolfgang <1965->  
Providence, Rhode Island : , : American Mathematical Society, , [2008]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
Autore Bertram Wolfgang <1965->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2008]
Descrizione fisica 1 online resource (218 p.)
Disciplina 510 s
512/.482
Collana Memoirs of the American Mathematical Society
Soggetto topico Infinite dimensional Lie algebras
Infinite-dimensional manifolds
Symmetric spaces
Geometry, Differential
ISBN 1-4704-0506-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""I. Basic notions""; ""1. Differential calculus""; ""2. Manifolds""; ""3. Tangent bundle and general fiber bundles""; ""4. The Lie bracket of vector fields""; ""5. Lie groups and symmetric spaces: basic facts""; ""II. Interpretation of tangent objects via scalar extensions""; ""6. Scalar extensions. I: Tangent functor and dual numbers""; ""7. Scalar extensions. II: Higher order tangent functors""; ""8. Scalar extensions. Ill: Jet functor and truncated polynomial rings""; ""III. Second order differential geometry""
""9. The structure of the tangent bundle of a vector bundle""""10. Linear connections. I: Linear structures on bilinear bundles""; ""11. Linear connections. II: Sprays""; ""12. Linear connections. Ill: Covariant derivative""; ""13. Natural operations. I: Exterior derivative of a one-form""; ""14. Natural operations. II: The Lie bracket revisited""; ""IV. Third and higher order differential geometry""; ""15. The structure of T[sup(k)]F: Multilinear bundles""; ""16. The structure of T[sup(k)]F: Multilinear connections""; ""17. Construction of multilinear connections""; ""18. Curvature""
""19. Linear structures on jet bundles""""20. Shifts and symmetrization""; ""21. Remarks on differential operators and symbols""; ""22. The exterior derivative""; ""V. Lie Theory""; ""23. The three canonical connections of a Lie group""; ""24. The structure of higher order tangent groups""; ""25. Exponential map and Campbell-Hausdorff formula""; ""26. The canonical connection of a symmetric space""; ""27. The higher order tangent structure of symmetric spaces""; ""VI.Diffeomorphism Groups and the exponential jet""; ""28. Group structure on the space of sections of T[sup(k)]M""
""29. The exponential jet for vector fields""""30. The exponential jet of a symmetric space""; ""31. Remarks on the exponential jet of a general connection""; ""32. From germs to jets and from jets to germs""; ""Appendix L. Limitations""; ""Appendix G. Generalizations""; ""Appendix: Multilinear Geometry""; ""BA. Bilinear algebra""; ""MA. Multilinear algebra""; ""SA. Symmetric and shift invariant multilinear algebra""; ""PG. Polynomial groups""; ""References""
Record Nr. UNINA-9910819101003321
Bertram Wolfgang <1965->  
Providence, Rhode Island : , : American Mathematical Society, , [2008]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui