Homotopy Theory and Related Topics Proceedings of the International

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1418 M. Mimura (Ed.)

Homotopy Theory and Related Topics Proceedings of the International Conference held at Kinosaki, Japan, August 19-24, 1988

Springer-Verlag Berlin Heidelberg NewYork LondonParis Tokyo Hong Kong

Editor

Mamoru Mimura Department of Mathematics Faculty of Science, Okayama University 3-1 Tsushima-Naka, Okayama, Japan 700

Mathematics Subject Classification (1980): 55-06 ISBN 3-540-52246-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-52246-8 Springer-Verlag New York Berlin Heidelberg

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© Springer-Verlag Berlin Heidelberg 1990 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper

Preface.

An international conference on HOMOTOPY THEORY AND RELATED TOPICS was held August 19-24, 1988 at the Kinosaki Conference Hall in Hyogo, Japan in honor of Professor Hirosi Toda who celebrated his sixtieth birthday on January 17, 1988.

His influence on the development of

homotopy theory has been enormous. The organizing committee consisted of A. Kono, Kyoto University M. Mahowald, Northwestern University M. Mimura, Okayama University K. Morisugi, Wakayama University G. Nishida, Kyoto University F.P. Peterson, Massachusetts Institute of Technology

The titles of the talks delivered at the conference are given below. The proceedings contain transcripts of some of the conference talks as well as rei at ed artie 1es.

A11 papers were refereed, and we take this opportunity

to thank the referees.

We would also like to express our gratitude to the

participants for their contributions to the conference and particularly to K. Iriye for help with various arrangements. Okayama, JAPAN September 1989 M. Mimura

CONTENTS Publications of Hirosi Toda •••••••••••••••••••••••••••••••••••• J.F. Adams

Talk

W.H. Lin

A conjecture of May on E term of the May spectral sequence for cohomology of the Steenrod algebra •••••••••••••••••••••••••••••••• 15

I.M. James

Continuous functions of several variables ••••••• 53

M. Tezuka N. Yagita

Cohomology of finite groups and Brown-Peterson cohomology I I ••••••••••••••••••••••••••••••••••• 57

J.R. Hubbuck

Some stably indecomposable loop spaces •••••••••• 70

D.J. Anick

R-local homotopy theory •••••••••••••••••••..•••• 78

on Toda's work ••••••••••••••••••••••••••••• 7

John McCleary Homotopy theory and closed geodesics •••••••••••• 86 Juno Mukai

A proof of the theorem characterizing the generalized J-homomorphism •••••••••••••••••••••• 95

R