Homotopy Theory : Tools and Applications.
Davis, Daniel G.
Homotopy Theory : Tools and Applications. - 1st ed. - 1 online resource (282 pages) - Contemporary Mathematics Series ; v.729 . - Contemporary Mathematics Series .
Cover -- Title page -- Contents -- Preface -- Plenary Talks -- Parallel Talks -- The -family in the (2)-local sphere at the prime 2 -- 1. Introduction -- 2. The -family in the Adams-Novikov Spectral Sequence -- 3. Subgroups of ₂ and the algebraic duality spectral sequence -- 4. The -family in the (2)-local sphere -- References -- A constructive approach to higher homotopy operations -- Introduction -- 1. The classical Toda Bracket -- 2. Graded Reedy Matching Spaces -- 3. General Definition of higher order operations -- 4. Separating Total Operations -- 5. Rigidifying Simplicial Diagrams up to Homotopy -- 6. Pointed higher operations -- 7. Long Toda Brackets and Massey Products -- 8. Fully reduced diagrams -- Appendix A. Background Material -- Appendix B. Indeterminacy -- References -- The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors -- 1. A crash course in -Tambara functors -- 2. Free -Tambara functors -- 3. Free ₂ Green and Tambara functors -- 4. The operadic right adjoint -- References -- The centralizer resolution of the (2)-local sphere at the prime 2 -- 1. Introduction -- 2. Important finite subgroups for Morava stabilizer groups at = =2 -- 3. The mod-2 cohomology algebra of ₂¹ -- 4. Algebraic centralizer resolutions -- 5. Topologically realizing the algebraic centralizer resolutions -- References -- Galois descent criteria -- Introduction -- 1. Profinite groups -- 2. Cosimplicial spaces -- 3. Pro-objects -- 4. Galois descent -- References -- Quantization of the modular functor and equivariant elliptic cohomology -- 1. Introduction -- 2. Background on Dominant -theory and the space -- 3. The equivariant sheaf ^ _ over ×Σ_ℂ, and locality -- 4. The sheaf ^ *(ℳ) over the universal elliptic curve, and Theta functions -- 5. Level representations of ⋉ and ^ ( / ). 6. Modularity of ^ (ℳ) -- 7. Some comments on our construction -- References -- Calculating obstruction groups for _ ring spectra -- 1. Introduction -- 2. Postnikov-based obstructions to commutativity -- 3. Background: Goerss-Hopkins obstruction theory -- 4. Homology-based obstructions to commutativity -- 5. Tools for calculation -- 6. Koszul duality -- 7. Filtrations and stability -- 8. The critical group and secondary operations -- 9. Calculation setup for -- 10. First calculations: =-1 -- 11. Further calculations: =0 -- 12. Further calculations: =1 -- 13. Further calculations: =2 -- 14. Final calculations in weight 2 -- References -- Comodules, sheaves, and the exact functor theorem -- 1. Even periodic ring spectra and formal groups -- 2. Cobordism comodules -- 3. Cobordism sheaves -- 4. Height -- 5. Landweber exactness -- References -- Complex orientations for of some perfectoid fields -- References -- String bordism and chromatic characteristics -- Introduction -- 1. Characteristics in chromatic homotopy theory -- 2. Chromatic and versal examples -- 3. K-theories -- 4. Topological modular forms -- 5. Bordism theories -- Acknowledgments -- References -- Mahowald square and Adams differentials -- 1. Introduction -- 2. The mod 2 Moore spectrum at stem 14-a warmup -- 3. ^-method for some Adams differentials in low stems -- 4. The Kahn-Priddy map and Toda brackets -- References -- Back Cover.
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17-21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
9781470452933
Goerss, Paul Gregory-Congresses.
Homotopy theory-Congresses.
Electronic books.
QA612.7 .H666 2019
514.24
Homotopy Theory : Tools and Applications. - 1st ed. - 1 online resource (282 pages) - Contemporary Mathematics Series ; v.729 . - Contemporary Mathematics Series .
Cover -- Title page -- Contents -- Preface -- Plenary Talks -- Parallel Talks -- The -family in the (2)-local sphere at the prime 2 -- 1. Introduction -- 2. The -family in the Adams-Novikov Spectral Sequence -- 3. Subgroups of ₂ and the algebraic duality spectral sequence -- 4. The -family in the (2)-local sphere -- References -- A constructive approach to higher homotopy operations -- Introduction -- 1. The classical Toda Bracket -- 2. Graded Reedy Matching Spaces -- 3. General Definition of higher order operations -- 4. Separating Total Operations -- 5. Rigidifying Simplicial Diagrams up to Homotopy -- 6. Pointed higher operations -- 7. Long Toda Brackets and Massey Products -- 8. Fully reduced diagrams -- Appendix A. Background Material -- Appendix B. Indeterminacy -- References -- The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors -- 1. A crash course in -Tambara functors -- 2. Free -Tambara functors -- 3. Free ₂ Green and Tambara functors -- 4. The operadic right adjoint -- References -- The centralizer resolution of the (2)-local sphere at the prime 2 -- 1. Introduction -- 2. Important finite subgroups for Morava stabilizer groups at = =2 -- 3. The mod-2 cohomology algebra of ₂¹ -- 4. Algebraic centralizer resolutions -- 5. Topologically realizing the algebraic centralizer resolutions -- References -- Galois descent criteria -- Introduction -- 1. Profinite groups -- 2. Cosimplicial spaces -- 3. Pro-objects -- 4. Galois descent -- References -- Quantization of the modular functor and equivariant elliptic cohomology -- 1. Introduction -- 2. Background on Dominant -theory and the space -- 3. The equivariant sheaf ^ _ over ×Σ_ℂ, and locality -- 4. The sheaf ^ *(ℳ) over the universal elliptic curve, and Theta functions -- 5. Level representations of ⋉ and ^ ( / ). 6. Modularity of ^ (ℳ) -- 7. Some comments on our construction -- References -- Calculating obstruction groups for _ ring spectra -- 1. Introduction -- 2. Postnikov-based obstructions to commutativity -- 3. Background: Goerss-Hopkins obstruction theory -- 4. Homology-based obstructions to commutativity -- 5. Tools for calculation -- 6. Koszul duality -- 7. Filtrations and stability -- 8. The critical group and secondary operations -- 9. Calculation setup for -- 10. First calculations: =-1 -- 11. Further calculations: =0 -- 12. Further calculations: =1 -- 13. Further calculations: =2 -- 14. Final calculations in weight 2 -- References -- Comodules, sheaves, and the exact functor theorem -- 1. Even periodic ring spectra and formal groups -- 2. Cobordism comodules -- 3. Cobordism sheaves -- 4. Height -- 5. Landweber exactness -- References -- Complex orientations for of some perfectoid fields -- References -- String bordism and chromatic characteristics -- Introduction -- 1. Characteristics in chromatic homotopy theory -- 2. Chromatic and versal examples -- 3. K-theories -- 4. Topological modular forms -- 5. Bordism theories -- Acknowledgments -- References -- Mahowald square and Adams differentials -- 1. Introduction -- 2. The mod 2 Moore spectrum at stem 14-a warmup -- 3. ^-method for some Adams differentials in low stems -- 4. The Kahn-Priddy map and Toda brackets -- References -- Back Cover.
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17-21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
9781470452933
Goerss, Paul Gregory-Congresses.
Homotopy theory-Congresses.
Electronic books.
QA612.7 .H666 2019
514.24