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The Atiyah-Patodi-Singer index theorem / Richard B. Melrose
| The Atiyah-Patodi-Singer index theorem / Richard B. Melrose |
| Autore | Melrose, Richard B. |
| Pubbl/distr/stampa | Wellesley : A. K. Peters, c1993 |
| Descrizione fisica | x, 377 p. : ill. ; 24 cm. |
| Disciplina | 514.74 |
| Collana | Research notes in mathematics, ISSN 07430337 ; 4 |
| Soggetto topico | Atiyah-Singer index theorem |
| ISBN | 1568810024 |
| Classificazione |
AMS 58J20
QA614.92.M45 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000705279707536 |
Melrose, Richard B.
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| Wellesley : A. K. Peters, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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The Atiyah-Singer index theorem : an introduction / Patrick Shanahan
| The Atiyah-Singer index theorem : an introduction / Patrick Shanahan |
| Autore | Shanahan, Patrick |
| Pubbl/distr/stampa | Berlin ; Heidelberg ; New York : Springer-Verlag, 1978 |
| Descrizione fisica | iv, 224 p. : ill. ; 25 cm. |
| Disciplina | 514.74 |
| Collana | Lecture notes in mathematics, 0075-8434 ; 638 |
| Soggetto topico |
Atiyah-Singer index theorem
Fixed point theory |
| ISBN | 3540086609 |
| Classificazione | AMS 58G10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000705349707536 |
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Shanahan, Patrick
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| Berlin ; Heidelberg ; New York : Springer-Verlag, 1978 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu
| The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu |
| Autore | Yu Yanlin |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 514.74 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Atiyah-Singer index theorem
Heat equation |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-95164-1
9786611951641 981-281-010-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation
2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| Record Nr. | UNINA-9910454372203321 |
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Yu Yanlin
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||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu
| The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu |
| Autore | Yu Yanlin |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 514.74 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Atiyah-Singer index theorem
Heat equation |
| ISBN |
1-281-95164-1
9786611951641 981-281-010-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation
2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| Record Nr. | UNINA-9910782394003321 |
|
Yu Yanlin
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The index theorem and the heat equation method / / Yanlin Yu
| The index theorem and the heat equation method / / Yanlin Yu |
| Autore | Yu Yanlin |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 514.74 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Atiyah-Singer index theorem
Heat equation |
| ISBN |
1-281-95164-1
9786611951641 981-281-010-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation
2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| Record Nr. | UNINA-9910825445803321 |
|
Yu Yanlin
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| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 / / Richard S. Palais
| Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 / / Richard S. Palais |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (379 pages) |
| Disciplina | 513.83 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Atiyah-Singer index theorem
Differential topology Homology theory |
| Soggetto non controllato |
Addition
Adjoint Algebraic topology Algebraic variety Almost complex manifold Arf invariant Asymptotic expansion Atiyah–Singer index theorem Automorphism Axiom Banach space Big O notation Boundary value problem Bounded operator Characteristic class Chern class Cohomology Cokernel Compact operator Complex vector bundle Computation Connected component (graph theory) Coordinate system Corollary Cotangent bundle Differentiable function Differentiable manifold Differential operator Dimension (vector space) Dimension Disjoint union Division by zero Elliptic operator Elliptic partial differential equation Equivalence class Euclidean space Euler class Exact sequence Existential quantification Fiber bundle Formal power series Fourier transform Fredholm operator Functional analysis Gelfand Grothendieck group H-cobordism Hilbert space Hodge theory Homogeneous polynomial Homomorphism Homotopy Indeterminate (variable) Injective function Integer Isomorphism class Jet bundle K-theory L-theory Linear map Manifold Michael Atiyah Natural transformation Normal bundle Orientability Pairing Partial differential equation Polynomial ring Polynomial Principal bundle Projection (mathematics) Riemann–Roch theorem Ring (mathematics) Robert M. Solovay Sign convention Singular integral Sobolev inequality Spanning tree Special case Subgroup Submanifold Subring Suggestion Summation Surjective function Symmetric bilinear form Symmetric function Tangent bundle Tangent space Tensor product Theorem Todd class Topological vector space Uniqueness theorem Vector bundle Vector space |
| ISBN | 1-4008-8204-4 |
| Classificazione | SK 350 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- CONTENTS -- PREFACE / Palais, Richard S. -- CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF / Borel, A. -- CHAPTER II. REVIEW OF K-THEORY / Solovay, Robert -- CHAPTER III. THE TOPOLOGICAL INDEX OF AN OPERATOR ASSOCIATED TO A G-STRUCTURE / Solovay, Robert -- CHAPTER IV. DIFFERENTIAL OPERATORS ON VECTOR BUNDLES / Palais, Richard S. -- CHAPTER V. ANALYTICAL INDICES OF SOME CONCRETE OPERATORS / Solovay, Robert M. -- CHAPTER VI. REVIEW OF FUNCTIONAL ANALYSIS / Palais, Richard S. -- CHAPTER VII. FREDHDIM OPERATORS / Palais, Richard S. -- CHAPTER VIII. CHAINS OP HILBERTIAN SPACES / Palais, Richard S. -- CHAPTER IX. THE DISCRETE SOBOLEV CHAIN OF A VECTOR BUNDLE / Palais, Richard S. -- CHAPTER X. THE CONTINUOUS SOBOLEV CHAIN OF A VECTOR BUNDLE / Palais, Richard S. -- CHAPTER XI. THE SEELEY ALGEBRA / Palais, Richard S. -- CHAPTER XII. HOMOTOPY INVARIANCE OF THE INDEX / Palaie, Richard S. -- CHAPTER XIII. WHITNEY SUMS / Palais, Richard S. -- CHAPTER XIV. TENSOR PRODUCTS / Palais, Richard S. -- CHAPTER XV. DEFINITION OF ia AND it ON K(M) / Solovay, Robert M. -- CHAPTER XVI. CONSTRUCTION OF Intk / Palais, R. S. / Seeley, R. T. -- CHAPTER XVII. COBORDISM INVARIANCE OP THE ANALYTICAL INDEX / Palais, R. S. / Seeley, R. T. -- CHAPTER XVIII. BORDISM GROUPS OF BUNDLES / Floyd, E. E. -- CHAPTER XIX. THE INDEX THEOREM: APPLICATIONS / Solovay, Robert M. -- APPENDIX I. THE INDEX THEOREM FOR MANIFOLDS WITH BOUNDARY / Atiyah, M. F. -- APPENDIX II. NON-STABLE CHARACTERISTIC CLASSES AND THE TOPOLOGICAL INDEX OP CLASSICAL ELLIPTIC OPERATORS / Shih, Weishu -- Backmatter |
| Record Nr. | UNINA-9910154746103321 |
| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Seminar on the Atiyah-Singer index theorem / [edited] by Richard S. Palais ; with contributions by M.F. Atiyah ... [et al.]
| Seminar on the Atiyah-Singer index theorem / [edited] by Richard S. Palais ; with contributions by M.F. Atiyah ... [et al.] |
| Autore | Institute for Advanced Study <Princeton, N.J.> |
| Pubbl/distr/stampa | Princeton : Princeton Univ. Press, 1965 |
| Descrizione fisica | x, 366 p. ; 24 cm. |
| Disciplina | 514.74 |
| Altri autori (Persone) |
Palais, Richard S.
Atiyah, Michael Francis |
| Collana | Annals of mathematics studies ; 57 |
| Soggetto topico |
Atiyah-Singer index theorem
Differential topology Homology theory |
| Classificazione | AMS 58-06 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001336069707536 |
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Institute for Advanced Study <Princeton, N.J.>
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| Princeton : Princeton Univ. Press, 1965 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Topologie und Analysis : Einfuhrung in die Atiyah-Singer-Indexformel / Bernhelm Booss
| Topologie und Analysis : Einfuhrung in die Atiyah-Singer-Indexformel / Bernhelm Booss |
| Autore | Booss, Bernhelm |
| Pubbl/distr/stampa | Berlin ; Heidelberg ; New York : Springer-Verlag, 1977 |
| Descrizione fisica | xiv, 352 p. : ill. ; 25 cm |
| Disciplina | 514.74 |
| Collana | Hochschultext |
| Soggetto topico |
Atiyah-Singer index theorem
Manifolds Operator theory |
| ISBN | 3540084517 |
| Classificazione |
AMS 58-02
LC QA329.B66 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ger |
| Record Nr. | UNISALENTO-991001452919707536 |
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Booss, Bernhelm
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| Berlin ; Heidelberg ; New York : Springer-Verlag, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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