Limit search to available items
Book Cover
Author Davis, Daniel G

Title Homotopy Theory
Published Providence : American Mathematical Society, 2019


Description 1 online resource (282 pages)
Series Contemporary Mathematics Ser. ; v. 729
Contemporary Mathematics Ser
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
Summary 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, an
Bibliography References
Notes Print version record
Subject Goerss, Paul Gregory -- Congresses
Homotopy theory -- Congresses
Homotopy theory.
Genre/Form Conference papers and proceedings.
Form Electronic book
Author Henn, Hans-Werner
Jardine, J. F
ISBN 9781470452933