Homotopy Theory
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 researc...
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| Format: | eBook |
| Language: | English |
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American Mathematical Society,
2019.
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| Series: | Contemporary Mathematics Ser.
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Table of Contents:
- 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 operations7. 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
- 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: =113. 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
- 3. The mod-2 cohomology algebra of ₂¹4. 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