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The Goodwillie tower and the EHP sequence / / Mark Behrens
| The Goodwillie tower and the EHP sequence / / Mark Behrens |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy groups
Algebraic topology Spectral sequences (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-9014-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Conventions""; ""Chapter 1. Dyer-Lashof operations and the identity functor""; ""1.1. The operadic bar construction""; ""1.2. The cooperadic structure on B()""; ""1.3. Operad structure on *(Id)""; ""1.4. Homology of extended powers""; ""1.5. Dyer-Lashof-like operations""; ""Chapter 2. The Goodwillie tower of the EHP sequence""; ""2.1. Fiber sequences associated to the EHP sequence""; ""2.2. Homological behavior of the fiber sequences""; ""2.3. Transfinite Atiyah-Hirzebruch spectral sequences""
""2.4. Transfinite Goodwillie spectral sequence""""Chapter 3. Goodwillie filtration and the P map""; ""3.1. Goodwillie filtration""; ""3.2. The genealogy of unstable elements""; ""3.3. Behavior of the E and P maps in the TAHSS""; ""3.4. Behavior of the E and P maps in the TGSS""; ""3.5. Detection in the TGSS""; ""3.6. Relationship with Whitehead products""; ""Chapter 4. Goodwillie differentials and Hopf invariants""; ""4.1. Hopf invariants and the transfinite EHPSS""; ""4.2. Stable Hopf invariants and metastable homotopy""; ""4.3. Goodwillie d1 differentials and stable Hopf invariants"" ""4.4. Higher Goodwillie differentials and unstable Hopf invariants""""4.5. Propagating differentials with the P and E maps""; ""4.6. Calculus form of the Whitehead conjecture""; ""4.7. Exotic Goodwillie differentials""; ""Chapter 5. EHPSS differentials""; ""5.1. EHPSS naming conventions""; ""5.2. Using the TGSS to compute the H map""; ""5.3. TEHPSS differentials from TGSS differentials""; ""5.4. A bad differential""; ""Chapter 6. Calculations in the 2-primary Toda range""; ""6.1. AHSS calculations""; ""6.2. Calculation of the GSS for S1""; ""6.3. GSS calculations"" ""6.4. Calculation of the EHPSS""""6.5. Tables of computations""; ""6.5.1. The AHSS for k(L(1))""; ""6.5.2. The AHSS for k(L(2))""; ""6.5.3. The AHSS for k(L(3))""; ""6.5.4. The EHPSS""; ""6.5.5. The GSS for n+1(S1)""; ""6.5.6. The GSS for n+2(S2)""; ""6.5.7. The GSS for n+3(S3)""; ""6.5.8. The GSS for n+4(S4)""; ""6.5.9. The GSS for n+5(S5)""; ""6.5.10. The GSS for n+6(S6)""; ""Appendix A. Transfinite spectral sequences associated to towers""; ""A.1. The Grothendieck group of ordinals""; ""A.2. Towers""; ""A.3. The transfinite homotopy spectral sequence of a tower"" ""A.4. Geometric boundary theorem""""Bibliography"" |
| Record Nr. | UNINA-9910480981103321 |
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Goodwillie tower and the EHP sequence / / Mark Behrens
| The Goodwillie tower and the EHP sequence / / Mark Behrens |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy groups
Algebraic topology Spectral sequences (Mathematics) |
| ISBN | 0-8218-9014-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Conventions""; ""Chapter 1. Dyer-Lashof operations and the identity functor""; ""1.1. The operadic bar construction""; ""1.2. The cooperadic structure on B()""; ""1.3. Operad structure on *(Id)""; ""1.4. Homology of extended powers""; ""1.5. Dyer-Lashof-like operations""; ""Chapter 2. The Goodwillie tower of the EHP sequence""; ""2.1. Fiber sequences associated to the EHP sequence""; ""2.2. Homological behavior of the fiber sequences""; ""2.3. Transfinite Atiyah-Hirzebruch spectral sequences""
""2.4. Transfinite Goodwillie spectral sequence""""Chapter 3. Goodwillie filtration and the P map""; ""3.1. Goodwillie filtration""; ""3.2. The genealogy of unstable elements""; ""3.3. Behavior of the E and P maps in the TAHSS""; ""3.4. Behavior of the E and P maps in the TGSS""; ""3.5. Detection in the TGSS""; ""3.6. Relationship with Whitehead products""; ""Chapter 4. Goodwillie differentials and Hopf invariants""; ""4.1. Hopf invariants and the transfinite EHPSS""; ""4.2. Stable Hopf invariants and metastable homotopy""; ""4.3. Goodwillie d1 differentials and stable Hopf invariants"" ""4.4. Higher Goodwillie differentials and unstable Hopf invariants""""4.5. Propagating differentials with the P and E maps""; ""4.6. Calculus form of the Whitehead conjecture""; ""4.7. Exotic Goodwillie differentials""; ""Chapter 5. EHPSS differentials""; ""5.1. EHPSS naming conventions""; ""5.2. Using the TGSS to compute the H map""; ""5.3. TEHPSS differentials from TGSS differentials""; ""5.4. A bad differential""; ""Chapter 6. Calculations in the 2-primary Toda range""; ""6.1. AHSS calculations""; ""6.2. Calculation of the GSS for S1""; ""6.3. GSS calculations"" ""6.4. Calculation of the EHPSS""""6.5. Tables of computations""; ""6.5.1. The AHSS for k(L(1))""; ""6.5.2. The AHSS for k(L(2))""; ""6.5.3. The AHSS for k(L(3))""; ""6.5.4. The EHPSS""; ""6.5.5. The GSS for n+1(S1)""; ""6.5.6. The GSS for n+2(S2)""; ""6.5.7. The GSS for n+3(S3)""; ""6.5.8. The GSS for n+4(S4)""; ""6.5.9. The GSS for n+5(S5)""; ""6.5.10. The GSS for n+6(S6)""; ""Appendix A. Transfinite spectral sequences associated to towers""; ""A.1. The Grothendieck group of ordinals""; ""A.2. Towers""; ""A.3. The transfinite homotopy spectral sequence of a tower"" ""A.4. Geometric boundary theorem""""Bibliography"" |
| Record Nr. | UNINA-9910788618403321 |
|
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Goodwillie tower and the EHP sequence / / Mark Behrens
| The Goodwillie tower and the EHP sequence / / Mark Behrens |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy groups
Algebraic topology Spectral sequences (Mathematics) |
| ISBN | 0-8218-9014-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Conventions""; ""Chapter 1. Dyer-Lashof operations and the identity functor""; ""1.1. The operadic bar construction""; ""1.2. The cooperadic structure on B()""; ""1.3. Operad structure on *(Id)""; ""1.4. Homology of extended powers""; ""1.5. Dyer-Lashof-like operations""; ""Chapter 2. The Goodwillie tower of the EHP sequence""; ""2.1. Fiber sequences associated to the EHP sequence""; ""2.2. Homological behavior of the fiber sequences""; ""2.3. Transfinite Atiyah-Hirzebruch spectral sequences""
""2.4. Transfinite Goodwillie spectral sequence""""Chapter 3. Goodwillie filtration and the P map""; ""3.1. Goodwillie filtration""; ""3.2. The genealogy of unstable elements""; ""3.3. Behavior of the E and P maps in the TAHSS""; ""3.4. Behavior of the E and P maps in the TGSS""; ""3.5. Detection in the TGSS""; ""3.6. Relationship with Whitehead products""; ""Chapter 4. Goodwillie differentials and Hopf invariants""; ""4.1. Hopf invariants and the transfinite EHPSS""; ""4.2. Stable Hopf invariants and metastable homotopy""; ""4.3. Goodwillie d1 differentials and stable Hopf invariants"" ""4.4. Higher Goodwillie differentials and unstable Hopf invariants""""4.5. Propagating differentials with the P and E maps""; ""4.6. Calculus form of the Whitehead conjecture""; ""4.7. Exotic Goodwillie differentials""; ""Chapter 5. EHPSS differentials""; ""5.1. EHPSS naming conventions""; ""5.2. Using the TGSS to compute the H map""; ""5.3. TEHPSS differentials from TGSS differentials""; ""5.4. A bad differential""; ""Chapter 6. Calculations in the 2-primary Toda range""; ""6.1. AHSS calculations""; ""6.2. Calculation of the GSS for S1""; ""6.3. GSS calculations"" ""6.4. Calculation of the EHPSS""""6.5. Tables of computations""; ""6.5.1. The AHSS for k(L(1))""; ""6.5.2. The AHSS for k(L(2))""; ""6.5.3. The AHSS for k(L(3))""; ""6.5.4. The EHPSS""; ""6.5.5. The GSS for n+1(S1)""; ""6.5.6. The GSS for n+2(S2)""; ""6.5.7. The GSS for n+3(S3)""; ""6.5.8. The GSS for n+4(S4)""; ""6.5.9. The GSS for n+5(S5)""; ""6.5.10. The GSS for n+6(S6)""; ""Appendix A. Transfinite spectral sequences associated to towers""; ""A.1. The Grothendieck group of ordinals""; ""A.2. Towers""; ""A.3. The transfinite homotopy spectral sequence of a tower"" ""A.4. Geometric boundary theorem""""Bibliography"" |
| Record Nr. | UNINA-9910817274203321 |
|
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological automorphic forms / / Mark Behrens, Tyler Lawson
| Topological automorphic forms / / Mark Behrens, Tyler Lawson |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (167 p.) |
| Disciplina | 515.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Automorphic forms
Algebraic topology Homotopy groups Shimura varieties |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0572-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background and motivation""; ""0.2. Subject matter of this book""; ""0.3. Organization of this book""; ""0.4. Acknowledgments""; ""Chapter 1. p-divisible groups""; ""1.1. Definitions""; ""1.2. Classification""; ""Chapter 2. The Honda-Tate classification""; ""2.1. Abelian varieties over finite fields""; ""2.2. Abelian varieties over Fp""; ""Chapter 3. Tate modules and level structures""; ""3.1. Tate modules of abelian varieties""; ""3.2. Virtual subgroups and quasi-isogenies""; ""3.3. Level structures""; ""3.4. The Tate representation""
""3.5. Homomorphisms of abelian schemes""""Chapter 4. Polarizations""; ""4.1. Polarizations""; ""4.2. The Rosati involution""; ""4.3. The Weil pairing""; ""4.4. Polarizations of B-linear abelian varieties""; ""4.5. Induced polarizations""; ""4.6. Classification of weak polarizations""; ""Chapter 5. Forms and involutions""; ""5.1. Hermitian forms""; ""5.2. Unitary and similitude groups""; ""5.3. Classification of forms""; ""Chapter 6. Shimura varieties of type U(1,n-1)""; ""6.1. Motivation""; ""6.2. Initial data""; ""6.3. Statement of the moduli problem"" ""6.4. Equivalence of the moduli problems""""6.5. Moduli problems with level structure""; ""6.6. Shimura stacks""; ""Chapter 7. Deformation theory""; ""7.1. Deformations of p-divisible groups""; ""7.2. Serre-Tate theory""; ""7.3. Deformation theory of points of Sh""; ""Chapter 8. Topological automorphic forms""; ""8.1. The generalized Hopkins-Miller theorem""; ""8.2. The descent spectral sequence""; ""8.3. Application to Shimura stacks""; ""Chapter 9. Relationship to automorphic forms""; ""9.1. Alternate description of Sh(Kp)""; ""9.2. Description of Sh(Kp)F""; ""9.3. Description of Sh(Kp)C"" ""9.4. Automorphic forms""""Chapter 10. Smooth G-spectra""; ""10.1. Smooth G-sets""; ""10.2. The category of simplicial smooth G-sets""; ""10.3. The category of smooth G-spectra""; ""10.4. Smooth homotopy fixed points""; ""10.5. Restriction, induction, and coinduction""; ""10.6. Descent from compact open subgroups""; ""10.7. Transfer maps and the Burnside category""; ""Chapter 11. Operations on TAF""; ""11.1. The E-action of GU(Ap,)""; ""11.2. Hecke operators""; ""Chapter 12. Buildings""; ""12.1. Terminology""; ""12.2. The buildings for GL and SL""; ""12.3. The buildings for U and GU"" ""Chapter 13. Hypercohomology of adele groups""""13.1. Definition of QGU and QU""; ""13.2. The semi-cosimplicial resolution""; ""Chapter 14. K(n)-local theory""; ""14.1. Endomorphisms of mod p points""; ""14.2. Approximation results""; ""14.3. The height n locus of Sh(Kp)""; ""14.4. K(n)-local TAF""; ""14.5. K(n)-local QU""; ""Chapter 15. Example: chromatic level 1""; ""15.1. Unit groups and the K(1)-local sphere""; ""15.2. Topological automorphic forms in chromatic filtration 1""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910480617703321 |
|
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological automorphic forms / / Mark Behrens, Tyler Lawson
| Topological automorphic forms / / Mark Behrens, Tyler Lawson |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (167 p.) |
| Disciplina | 515.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Automorphic forms
Algebraic topology Homotopy groups Shimura varieties |
| ISBN | 1-4704-0572-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background and motivation""; ""0.2. Subject matter of this book""; ""0.3. Organization of this book""; ""0.4. Acknowledgments""; ""Chapter 1. p-divisible groups""; ""1.1. Definitions""; ""1.2. Classification""; ""Chapter 2. The Honda-Tate classification""; ""2.1. Abelian varieties over finite fields""; ""2.2. Abelian varieties over Fp""; ""Chapter 3. Tate modules and level structures""; ""3.1. Tate modules of abelian varieties""; ""3.2. Virtual subgroups and quasi-isogenies""; ""3.3. Level structures""; ""3.4. The Tate representation""
""3.5. Homomorphisms of abelian schemes""""Chapter 4. Polarizations""; ""4.1. Polarizations""; ""4.2. The Rosati involution""; ""4.3. The Weil pairing""; ""4.4. Polarizations of B-linear abelian varieties""; ""4.5. Induced polarizations""; ""4.6. Classification of weak polarizations""; ""Chapter 5. Forms and involutions""; ""5.1. Hermitian forms""; ""5.2. Unitary and similitude groups""; ""5.3. Classification of forms""; ""Chapter 6. Shimura varieties of type U(1,n-1)""; ""6.1. Motivation""; ""6.2. Initial data""; ""6.3. Statement of the moduli problem"" ""6.4. Equivalence of the moduli problems""""6.5. Moduli problems with level structure""; ""6.6. Shimura stacks""; ""Chapter 7. Deformation theory""; ""7.1. Deformations of p-divisible groups""; ""7.2. Serre-Tate theory""; ""7.3. Deformation theory of points of Sh""; ""Chapter 8. Topological automorphic forms""; ""8.1. The generalized Hopkins-Miller theorem""; ""8.2. The descent spectral sequence""; ""8.3. Application to Shimura stacks""; ""Chapter 9. Relationship to automorphic forms""; ""9.1. Alternate description of Sh(Kp)""; ""9.2. Description of Sh(Kp)F""; ""9.3. Description of Sh(Kp)C"" ""9.4. Automorphic forms""""Chapter 10. Smooth G-spectra""; ""10.1. Smooth G-sets""; ""10.2. The category of simplicial smooth G-sets""; ""10.3. The category of smooth G-spectra""; ""10.4. Smooth homotopy fixed points""; ""10.5. Restriction, induction, and coinduction""; ""10.6. Descent from compact open subgroups""; ""10.7. Transfer maps and the Burnside category""; ""Chapter 11. Operations on TAF""; ""11.1. The E-action of GU(Ap,)""; ""11.2. Hecke operators""; ""Chapter 12. Buildings""; ""12.1. Terminology""; ""12.2. The buildings for GL and SL""; ""12.3. The buildings for U and GU"" ""Chapter 13. Hypercohomology of adele groups""""13.1. Definition of QGU and QU""; ""13.2. The semi-cosimplicial resolution""; ""Chapter 14. K(n)-local theory""; ""14.1. Endomorphisms of mod p points""; ""14.2. Approximation results""; ""14.3. The height n locus of Sh(Kp)""; ""14.4. K(n)-local TAF""; ""14.5. K(n)-local QU""; ""Chapter 15. Example: chromatic level 1""; ""15.1. Unit groups and the K(1)-local sphere""; ""15.2. Topological automorphic forms in chromatic filtration 1""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910788857303321 |
|
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological automorphic forms / / Mark Behrens, Tyler Lawson
| Topological automorphic forms / / Mark Behrens, Tyler Lawson |
| Autore | Behrens Mark <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (167 p.) |
| Disciplina | 515.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Automorphic forms
Algebraic topology Homotopy groups Shimura varieties |
| ISBN | 1-4704-0572-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background and motivation""; ""0.2. Subject matter of this book""; ""0.3. Organization of this book""; ""0.4. Acknowledgments""; ""Chapter 1. p-divisible groups""; ""1.1. Definitions""; ""1.2. Classification""; ""Chapter 2. The Honda-Tate classification""; ""2.1. Abelian varieties over finite fields""; ""2.2. Abelian varieties over Fp""; ""Chapter 3. Tate modules and level structures""; ""3.1. Tate modules of abelian varieties""; ""3.2. Virtual subgroups and quasi-isogenies""; ""3.3. Level structures""; ""3.4. The Tate representation""
""3.5. Homomorphisms of abelian schemes""""Chapter 4. Polarizations""; ""4.1. Polarizations""; ""4.2. The Rosati involution""; ""4.3. The Weil pairing""; ""4.4. Polarizations of B-linear abelian varieties""; ""4.5. Induced polarizations""; ""4.6. Classification of weak polarizations""; ""Chapter 5. Forms and involutions""; ""5.1. Hermitian forms""; ""5.2. Unitary and similitude groups""; ""5.3. Classification of forms""; ""Chapter 6. Shimura varieties of type U(1,n-1)""; ""6.1. Motivation""; ""6.2. Initial data""; ""6.3. Statement of the moduli problem"" ""6.4. Equivalence of the moduli problems""""6.5. Moduli problems with level structure""; ""6.6. Shimura stacks""; ""Chapter 7. Deformation theory""; ""7.1. Deformations of p-divisible groups""; ""7.2. Serre-Tate theory""; ""7.3. Deformation theory of points of Sh""; ""Chapter 8. Topological automorphic forms""; ""8.1. The generalized Hopkins-Miller theorem""; ""8.2. The descent spectral sequence""; ""8.3. Application to Shimura stacks""; ""Chapter 9. Relationship to automorphic forms""; ""9.1. Alternate description of Sh(Kp)""; ""9.2. Description of Sh(Kp)F""; ""9.3. Description of Sh(Kp)C"" ""9.4. Automorphic forms""""Chapter 10. Smooth G-spectra""; ""10.1. Smooth G-sets""; ""10.2. The category of simplicial smooth G-sets""; ""10.3. The category of smooth G-spectra""; ""10.4. Smooth homotopy fixed points""; ""10.5. Restriction, induction, and coinduction""; ""10.6. Descent from compact open subgroups""; ""10.7. Transfer maps and the Burnside category""; ""Chapter 11. Operations on TAF""; ""11.1. The E-action of GU(Ap,)""; ""11.2. Hecke operators""; ""Chapter 12. Buildings""; ""12.1. Terminology""; ""12.2. The buildings for GL and SL""; ""12.3. The buildings for U and GU"" ""Chapter 13. Hypercohomology of adele groups""""13.1. Definition of QGU and QU""; ""13.2. The semi-cosimplicial resolution""; ""Chapter 14. K(n)-local theory""; ""14.1. Endomorphisms of mod p points""; ""14.2. Approximation results""; ""14.3. The height n locus of Sh(Kp)""; ""14.4. K(n)-local TAF""; ""14.5. K(n)-local QU""; ""Chapter 15. Example: chromatic level 1""; ""15.1. Unit groups and the K(1)-local sphere""; ""15.2. Topological automorphic forms in chromatic filtration 1""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910829067703321 |
|
Behrens Mark <1975->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||