Algebraic Topology and Algebraic K-Theory: Proceedings of a Conference October 24-28, 1983, at Princeton University, Dedicated to John C. Moore on His 60th Birthday

578 Pages·1987·57.11 MB·English

by  William Browder

Annals of Mathematics Studies
Number 113

ALGEBRAIC TOPOLOGY AND
ALGEBRAIC K-THEORY
EDITED BY
WILLIAM BROWDER
Proceedings of a conference October 24-28, 1983,
at Princeton University, dedicated to
John C. Moore on his 60th birthday
PRINCETON UNIVERSITY PRESS
PRINCETON, NEW JERSEY
1987
Copyright © 1987 by Princeton University Press
ALL RIGHTS RESERVED
The Annals of Mathematics Studies are edited by
William Browder, Robert P. Langlands, John Milnor, and Elias M. Stein
Corresponding editors:
Stefan Hildebrandt, H. Blaine Lawson, Louis Nirenberg, and David Vogan
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Printed in the United States of America
by Princeton University Press, 41 William Street
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☆
Library of Congress Cataloging in Publication data will
be found on the last printed page of this book
DEDICATION TO JOHN MOORE
John Moore, in his mathematical career and his more
than 30 years at Princeton, has made a lasting impact on
the subject of topology, both in his research and in his
influence on the many graduate students who worked with
him. This conference and this volume are dedicated to him
in recognition and warm appreciation by his ex-students, by
other coworkers in topology, and by his many friends,
numbered in both groups.
Students of John Moore
Richard Swan 1957
William Browder 1958
James Stasheff 1961
Allan Clark 1961
Stephen Weingram 1962
Paul Baum 1962
Wu-yi Hsiang 1964
J. Peter May 1964
William Singer 1967
Harsh V. Pittie 1970
Fred William Roush 1972
Harold Hastings 1972
Joseph Neisendorfer 1972
Brian Smith 1972
Philip Trauber 1973
James Lin 1974
Haynes Miller 1975
Leo Chouinard 1975
Robert Thomason 1977
Paul Selick 1977
John Long 1979
v
LIST OF SPEAKERS AT THE CONFERENCE
J. F. Adams
D. Anick
E. H. Brown
G. Carlsson
F. Cohen
R. Cohen
W. Dwyer
E. Friedlander
S. Halperin
D. Kan
J. Lin
M. Mahowald
H. Miller
J. C. Moore
J. Neisendorfer
F. P. Peterson
D. Ravene1
P. Selick
J.-P. Serre
W. Singer
C. Soule
J. Stasheff
R. Swan
R. Thomason
F. Waldhaussen
A. Zabrodsky
CONTENTS
Preface ix
I EXPONENTS IN HOMOTOPY THEORY 3
by F. R. Cohen, J. C. Moore, and
J. A. Neisendorfer
II THE EXPONENT OF A MOORE SPACE 35
by Joseph A. Neisendorfer
III THE SPACE OF MAPS OF MOORE SPACES INTO SPHERES 72
by H. E. A. Campbell, F. R. Cohen,
F. P. Peterson, and P. S. Selick
IV THE ADAMS SPECTRAL SEQUENCE OF Q2S3 AND
BROWN- GITLER SPECTRA 101
by Edgar H. Brown and Ralph L. Cohen
V HOMOTOPY GROUPS OF SOME MAPPING TELESCOPES 126
by Donald M. Davis and Mark Mahowald
VI MAPPING TELESCOPES AND K^-LOCALIZATION 152
by Donald M. Davis, Mark Mahowald and
Haynes Miller
VII THE GEOMETRIC REALIZATION OF THE CHROMATIC
RESOLUTION 168
by Douglas C. Ravenel
VIII EQUIVALENCES BETWEEN HOMOTOPY THEORIES OF
DIAGRAMS 180
by W. G. Dwyer and D. M. Kan
IX THE ROLE OF THE STEENROD ALGEBRA IN THE
MOD 2 COHOMOLOGY OF A FINITE H-SPACE 206
by James P. Lin
X MAPS BETWEEN CLASSIFYING SPACES 228
by A. Zabrodsky
XI GENERIC ALGEBRAS AND CW COMPLEXES 247
by David J. Anick
vii
viii CONTENTS
XII DEFORMATION THEORY AND THE LITTLE
CONSTRUCTIONS OF CARTAN AND MOORE 322
by James Stasheff
XIII FREE (Z2)3 - ACTIONS ON FINITE COMPLEXES 332
by Gunnar CarIsson
XIV EQUIVARIANT CONSTRUCTIONS OF NONEQUIVARIANT
SPECTRA 345
by J. P. May
XV A DECOMPOSITION OF THE SPACE OF GENERALIZED
MORSE FUNCTIONS 365
by Ralph L. Cohen
XVI ALGEBRAIC K-THEORY OF SPACES, CONCORDANCE
AND STABLE HOMOTOPY THEORY 392
by Friedhelm Waldhausen
XVII THE MAP BSG -> A(*) -» QS° 418
by Marcel Bokstedt and Friedhelm Waldhausen
XVIII VECTOR BUNDLES, PROJECTIVE MODULES AND THE
K-THEORY OF SPHERES 432
by Richard G. Swan
XVIX LIMITS OF INFINITESMAL GROUP COHOMOLOGY 523
by Eric M. Friedlander and Brian J. Parshall
XX ALGEBRAIC K-THEORY OF GROUP SCHEME ACTIONS 539
by R. W. Thomason
PREFACE
From October 24 to October 28, 1983, a conference entitled
'Algebraic Topology and Algebraic K-theory’ was held at
Princeton University, and was dedicated to John Moore on his
60th birthday. It was planned by an organizing committee
consisting of William Browder, chairman, Franklin P. Peterson,
James Stasheff and Richard Swan.
It was the intention of the organizers to organize a
conference that emphasized homotopy theory, algebraic topology
more generally and some more topologically related aspects of
algebraic K-theory, and to create an interesting conference
with a relatively narrow focus, without trying to cover all
aspects of topology, or even of algebraic topology.
Neither was it the intention of the committee to try to
reflect explicitly the interests of Moore, or to emphasize
explicitly his role and that of his students in so many of the
modern developments. In the event, these things were, in fact,
well displayed during the conference.
The conference was part of a special year in Algebraic
Topology and K-theory at Princeton University during the
1983-84 academic year, which was supported by the National
Science Foundation.
Special thanks are due to Nancy Schlesinger who handled
most of the day to day organization of the conference, as well
as to a large number of Princeton graduate students who pitched
in to help with refreshments, and other aspects of hospitality
for the visitors.
W. Browder
ix