**Contemporary Mathematics**

Volume: 346;
2004;
507 pp;
Softcover

MSC: Primary 55; 57; 20;

Print ISBN: 978-0-8218-3285-1

Product Code: CONM/346

List Price: $131.00

Individual Member Price: $104.80

**Electronic ISBN: 978-0-8218-7936-8
Product Code: CONM/346.E**

List Price: $131.00

Individual Member Price: $104.80

# Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Share this page *Edited by *
*Paul Goerss; Stewart Priddy*

As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics.

This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic \(K\)-theory, and \(\mathbb{A}^1\) homotopy theory. Among the contributors to the volume were Alejandro Adem, Ralph L. Cohen, Jean-Louis Loday, and many others.

The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.

#### Table of Contents

# Table of Contents

## Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

- Contents v6 free
- Preface vii8 free
- Constructing and deconstructing group actions 110 free
- On the existence of the self map υ92 on the Smith-Toda complex V (1) at the prime 3 918
- 1. Introduction and statement of results 918
- 2. The Adams spectral sequence of eo2 Λ V(1) 1322
- 3. Calculation of the Adams E2 term ExtA. (F3, H*(V(1))) 2029
- 4. The splitting of D(V(1)) Λ V(1) 2433
- 5. The product rule 2635
- 6. Selected AHSS calculations of π * (V (1)) 2938
- 7. The order of the βI action on V(1) 3342
- 8. Proof that υ92 is a permanent cycle 3443
- 9. Proof that υ92 extends over V(1) 4049
- References 4857

- The theory of p-local groups: a survey 5160
- 1. The p-completion functor 5463
- 2. Fusion and linking systems of finite groups 5564
- 2.1. Fusion systems of groups 5564
- 2.2. Centric linking systems of groups 5665
- 2.3. Homotopy Equivalences of p-completed classifying spaces 5665
- 2.4. Maps from classifying spaces of finite p-groups 5766
- 2.5. Fusion and linking systems for spaces 5867
- 2.6. Isotypical equivalences of fusion and linking categories 5968
- 2.7. Self homotopy equivalences of BGΛp 5968

- 3. The Martino-Priddy conjecture 5968
- 4. Abstract finite fusion and linking systems 6473
- 4.1. Fusion systems 6473
- 4.2. Centric linking systems 6574
- 4.3. p-local finite groups 6675
- 4.4. Centralizers and mapping spaces 6776
- 4.5. Homology decompositions 6877
- 4.6. Cohomology of the classifying space 6978
- 4.7. Fusion and linking systems determined by their classifying space 7180
- 4.8. Existence and uniqueness of linking systems 7281

- 5. Examples and methods of construction 7382
- 6. p-local compact groups 7887
- References 8392

- Fourier decompositions of loop bundles 8594
- Weak equivalences of simplicial presheaves 97106
- Koszul duality of operads and homology of partition posets 115124
- Prologue and introduction 115124
- 0. Conventions 120129
- 1. Composition products and operad structures 123132
- 2. Chain complexes of modules over an operad 137146
- 3. The reduced bar construction 154163
- 4. Bar constructions with coefficients 172181
- 5. Koszul duality for operads 194203
- 6. Epilogue: partition posets 204213
- References 209218
- Glossary and notation index 212221

- On K*(Z) and classical conjectures in the arithmetic of cyclotomic fields 217226
- Finite group actions in elliptic cohomology 239248
- Topological Hochschild homology and the de Rham-Witt complex for Z(P) -algebras 253262
- Homotopy theory of comodules over a Hopf algebroid 261270
- Bousfield's E2 model theory for simplicial objects 305314
- A relation between the Picard group of the E(n)-local homotopy category and E(n)-based Adams spectral sequence 321330
- Homotopy limits of monad algebras 335344
- Trialgebras and families of polytopes 369378
- Equivariant symmetric spectra 399408
- Gamma homology of group algebras and of polynomial algebras 453462
- Formality and S1-equivariant algebraic models 463472
- A convenient model category for commutative ring spectra 473482
- The Tate-Farrell cohomology of the Morava stabilizer group Sp– 1 with coefficients in Ep–1 485494
- Characterizing simplicial commutative algebras with vanishing André-Quillén homology 493502

#### Readership

Graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.