**Contemporary Mathematics**

Volume: 265;
2000;
249 pp;
Softcover

MSC: Primary 55;
Secondary 00; 13; 18; 19; 20; 57

Print ISBN: 978-0-8218-2078-0

Product Code: CONM/265

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

**Electronic ISBN: 978-0-8218-7855-2
Product Code: CONM/265.E**

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

# Une Dégustation Topologique: Homotopy Theory in the Swiss Alps

Share this page *Edited by *
*Dominique Arlettaz; Kathryn Hess*

The talks given at the Arolla Conference on Algebraic Topology covered a broad spectrum of current research in homotopy theory, offering participants the possibility to sample and relish selected morsels of homotopy theory, much as a participant in a wine tasting partakes of a variety of fine wines. True to the spirit of the conference, the proceedings included in this volume present a savory sampler of homotopical delicacies. Readers will find within these pages a compilation of articles describing current research in the area, including classical stable and unstable homotopy theory, configuration spaces, group cohomology, K-theory, localization, \(p\)-compact groups, and simplicial theory.

#### Readership

Graduate students and research mathematicians interested in homotopy theory; algebraic topologists.

# Table of Contents

## Une Degustation Topologique: Homotopy Theory in the Swiss Alps

- Contents vii8 free
- Photo of Arolla ix10 free
- Preface x11 free
- Conference photo xii13 free
- List of talks xiv15 free
- List of participants xvi17 free
- Homological localizations preserve 1-connectivity 124 free
- Some free modules over the cohomology of K(Z/2Z, n): A short walk in the Alps 730
- Some remarks concerning degree zero complete cohomology 2144
- Two completion towers for generalized homology 2750
- André-Quillen (co-)homology for simplicial algebras over simplicial operads 4164
- An alternative approach to homology 87110
- Homotopical syzygies 99122
- K-theory hypercohomology spectra of number rings at the prime 2 129152
- A survey of Anick-Gray-Theriault constructions and applications to the exponent theory of spheres and Moore spaces 159182
- Invariant theory and the K-theory of the Dwyer-Wilkerson space 175198
- Algebraic K-theory spectra of non-exceptional two-regular number fields 187210
- The microstable Adams-Novikov spectral sequence 193216
- 1. Introduction 193216
- 2. Empirical evidence: similarities among the groups π*(T(m)) 194217
- 3. The bigraded Hopf algebroid (A, Г) 196219
- 4. Maps from subalgebras Г to the f(m + 1) 201224
- 5. The microchromatic spectral sequence 203226
- 6. The microstable 0- and 1-lines 206229
- 7. The Thorn reduction 207230
- References 209232

- Iterating series of localization functors 211234
- E8 is a totally N-determined 5-compact group 223246
- On orbit configuration spaces and the rational cohomology of F(RPn, k) 233256