**Contemporary Mathematics**

Volume: 271;
2001;
321 pp;
Softcover

MSC: Primary 55;

Print ISBN: 978-0-8218-2621-8

Product Code: CONM/271

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

**Electronic ISBN: 978-0-8218-7861-3
Product Code: CONM/271.E**

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

# Homotopy Methods in Algebraic Topology

Share this page *Edited by *
*J. P. C. Greenlees; Robert R. Bruner; Nicholas Kuhn*

with assistance from Robert R. Bruner, Wayne State University, Detroit, MI, and Nicholas Kuhn, University of Virginia, Charlottesville

This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, \(p\)-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the \(E_{\infty}\) tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.

#### Readership

Graduate students and research mathematicians interested in algebraic topology.

# Table of Contents

## Homotopy Methods in Algebraic Topology

- Contents vii8 free
- Preface ix10 free
- Speakers xi12 free
- Participants xiii14 free
- Conference photo xvi17 free
- A brief introduction to the work of J. Peter May, on the occasion of his 60th birthday xix20 free
- Mathematical ancestry of J. Peter May xliii44 free
- On the Adams E2-term for elliptic cohomology 146 free
- Mapping class groups and function spaces 1762
- Extended powers of manifolds and the Adams spectral sequence 4186
- Centers and Coxeter elements 5398
- On the homotopy type of the loops on a 2-cell complex 77122
- Rational SO(3)-equivariant cohomology theories 99144
- 1. Introduction. 99144
- 2. The closed subgroups of 80(3). 101146
- 3. Burnside splitting. 104149
- 4. Stable isotropy groups. 106151
- 5. Free G-spectra. 107152
- 6. Reduction to normalizers. 109154
- 7. The algebraic model of the category of (G, c)-spectra. 112157
- 8. The fibres. 115160
- 9. Mackey functors. 117162
- 10. The ordinary part of the model. 119164
- 11. Reduction to the Weyl group. 122167
- References 124169

- On the K-theory of nilpotent endomorphisms 127172
- The Ext0-term of the real-oriented Adams-Novikov spectral sequence 141186
- Toral groups and classifying spaces of p-compact groups 155200
- Stable splittings and the diagonal 169214
- Dual calculus for functors to spectra 183228
- The triple loop space approach to the telescope conjecture 217262
- Flatness for the E∞ tensor product 285330
- On the Connes-Kreimer construction of Hopf algebras 311356