Homotopy theory : tools and applications : a conference in honor of Paul Goerss's 60th birthday, July 17-21, 2017, University of Illinois at Urbana-Champaign, Urbana, Illinois / Daniel G. Davis [and four others], editors.

Format:

Book

Author/Creator:

Davis, Daniel G.

Contributor:

Goerss, Paul Gregory, honouree.

Davis, Daniel G., 1972- editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 729

Contemporary mathematics, 729 0271-4132

Language:

English

Subjects (All):

Goerss, Paul Gregory--Congresses.

Goerss, Paul Gregory.

Homotopy theory--Congresses.

Homotopy theory.

Physical Description:

1 online resource (xi, 268 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2019]

Language Note:

English

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, and the theory of higher homotopy operations.

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 operations

7. Long Toda Brackets and Massey Products

8. Fully reduced diagrams

Appendix A. Background Material

Appendix B. Indeterminacy

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

The centralizer resolution of the (2)-local sphere at the prime 2

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

Galois descent criteria

1. Profinite groups

2. Cosimplicial spaces

3. Pro-objects

4. Galois descent

Quantization of the modular functor and equivariant elliptic cohomology

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

Calculating obstruction groups for _{∞} ring spectra

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

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

Complex orientations for of some perfectoid fields

String bordism and chromatic characteristics

1. Characteristics in chromatic homotopy theory

2. Chromatic and versal examples

3. K-theories

4. Topological modular forms

5. Bordism theories

Acknowledgments

Mahowald square and Adams differentials

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

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5293-6