# Algebraic Topology: Oaxtepec 1991

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*Martin C. Tangora*

This book consists of twenty-nine articles contributed by participants of an International Conference in Algebraic Topology held in July 1991 in Oaxtepec, Mexico. In addition to papers on current research, there are several surveys and expositions on the work of Mark Mahowald, whose sixtieth birthday was celebrated during the conference. The conference was truly international, with over 130 mathematicians from fifteen countries. It ended with a spectacular total eclipse of the sun, a photograph of which appears as the frontispiece. The papers range over much of algebraic topology and cross over into related areas, such as \(K\)-theory, representation theory, and Lie groups. Also included is a chart of the Adams spectral sequence and a bibliography of Mahowald's publications.

#### Readership

Mathematicians interested in algebraic topology and related fields of research.

# Table of Contents

## Algebraic Topology: Oaxtepec 1991

- Contents vii8 free
- Preface xi12 free
- List of speakers xiii14 free
- List of participants xv16 free
- Mark Mahowald's work on the homotopy groups of spheres 120 free
- Immersions of projective spaces: a historical survey 3150
- Abelian II-algebras and their projective dimension 3958
- Modular representations on the homology of powers of real projective space 4968
- Ext in the nineties 7190
- On the representation theory associated to the cohomology of configuration spaces 91110
- Hopf algebras, Witt vectors, and Brown-Gitler spectra 111130
- v2 periodic homotopy families 129148
- Stable splittings for classifying spaces of alternating, special orthogonal and special unitary groups 143162
- On the homotopy type of configuration complexes 159178
- The ring structure of BoP* 171190
- Projectivity of the Whitehead product in spheres II 199218
- Dihedral homology and homotopy fixed point sets 215234
- ΩSU (n) does not split in 2 suspensions, for n ≥ 3 225244
- The Adams-Novikov spectral sequence for the L2 localization of a v2 spectrum 237256
- The topology of rational maps to Grassmannians and a homotopy theoretic proof of the Kirwan stability theorem 251270
- Obstructions for a map to be cyclic 277296
- Loop spaces and phantom maps 297316
- K -theory and the homotopy types of some function spaces 309328
- On the double transfer 339358
- Some examples of Hopf Algebras and Tannakian categories 349368
- The Hurewicz homomorphism of the compact exceptional Lie group E6 361380
- Periodic behavior of ΣCpoo and its applications 369388
- On the orientability of bundles and fibrations: the obstruction theory and applications to K, KO and Morava K-theories 383402
- Hopkins' and Mahowald's picture of Shimomura's v1-Bockstein spectral sequence calculation 407426
- Some remarks on products in Ext 419438
- A relation between K-theory and unstable homotopy groups with 431an application to BA relation between K-theory and unstable homotopy groups with BΣP 431450
- Graded G-sets, symmetric powers of permutation modules, and the cohomology of wreath products 441460
- Nilpotent elements in the Bockstein spectral sequence for BSpin(n) 453472
- Appendix 1: The publications of Mark Mahowald 471490
- Appendix 2: Adams Spectral Sequence chart 479498