Algebraic Topology: New Trends in Localization and Periodicity: Barcelona Conference on Algebraic Topology, Sant Feliu de Guíxols, Spain, June 1–7, 1994

404 Pages·1996·10.08 MB·English

by  Martin Arkowitz

Progress in Mathematics
Volume 136
Series Editors
H. Bass
J. Oesterle
A. Weinstein
Algebraic Topology:
New Trends
in Localization
and Periodicity
Barcelona Conference on Algebraic Topology,
Sant Feliu de Guixols, Spain, June 1-7, 1994
Carles Broto
Carles Casacuberta
Guido Mislin
Editors
Birkhauser Verlag
Basel· Boston· Berlin
Editors:
Carles Broto and Carles Casacuberta
Departament de Matematiques
Universitat Autonoma de Barcelona
E-08193 Bellaterra
Spain
Guido Mislin
Mathematik
ETHZentrum
8092 Zurich
Switzerland
A CIP catalogue record for this book is available from the Library of Congress,
Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Algebraic topology: new trends in localization and periodicity /
Barcelona Conference on Algebraic Topology, Sant Feliu de
Guixols, Spain, June 1-7, 1994. Carles Broto ... ed. - Basel ;
Boston ; Berlin : Birkhauser, 1996
(Progress in mathematics ; Vol. 136)
ISBN-13: 978-3-0348-9869-0 e-ISBN-13: 978-3-0348-9018-2
DOl: 10.1007/978-3-0348-9018-2
NE: Broto, Carles [Hrsg.]; Barcelona Conference on Algebraic Topology
<1994>; GT
AMS-Classification 55P60.
This work is subject to copyright. All rights are reserved, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, re-use
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owner must be obtained.
© 1996 Birkhauser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland
Softcover reprint of the hardcoverlst edition 1996
Printed on acid-free paper produced of chlorine-free pulp. TCF
00
987654321
Table of contents
Foreword ............................................................. vii
List of Participants ................................................... viii
Titles of Talks ........................................................ Xll
M. Arkowitz and G. Lupton, On the nilpotency of subgroups of
self-homotopy equivalences ....................................... 1
D. Arlettaz and P. Zelewski, Linear group homology properties of
the inclusion of a ring of integers into a number field ............ 23
A. K. Bousfield, Unstable localization and periodicity ................. 33
M. Brunetti, On the canonical GL2(F2)-module structure of
K(n)*(B7!./2 x B7!./2) ........................................... 51
A. Cavicchioli and F. Hegenbarth, Manifolds with highly
connected universal covers ....................................... 61
B. Cenkl and M. Vigue-Poirrier, Hochschild and cyclic
homology of an almost commutative cochain algebra associated
to a nilmanifold ................................................. 69
W. ChachOlski, Closed classes ....................................... 95
F. R. Cohen, On mapping class groups from a homotopy
theoretic point of view ........................................... 119
M. C. Crabb and J. R. Hubbuck, Representations of the
homology of BV and the Steenrod algebra II ..................... 143
K. Dekimpe and P. Igodt, Polynomial structures for iterated
central extensions of abelian-by-nilpotent groups .................. 155
W. G. Dwyer, The centralizer decomposition of BG .................. 167
H. H. Glover, I. J. Leary, and C. B. Thomas, The Yagita invariant
of general linear groups ......................................... 185
I. M. James, Fibrewise complexes .................................... 193
A. Jeanneret, P. S. Landweber, and D. C. Ravenel, A note on the
thick subcategory theorem ........................................ 201
T. Kashiwabara, N. Strickland, and P. Turner, The Morava K-theory
Hopf ring for BP ............................................... 209
vi Contents
K. Y. Lam and D. Randall, Periodicity of geometric dimension for
real projective spaces ............................................ 223
L. Langsetmo, Further structure in K(1)s!kS2n+1 ................... 235
J. Lannes and S. Zarati, Tor et Ext-dimensions des H*V -A-modules
instables qui sont de type fini comme H*V -modules .............. 241
I. J. Leary, A bound on the exponent of the cohomology of
Be -bundles ..................................................... 255
R. Levi, A counter-example to a conjecture of Cohen ................. 261
I. Llerena and N. H. V. Hu'ng, The complete Steenrod algebra and
the generalized Dickson algebra .................................. 271
C. A. McGibbon, On the localization genus of a space ................ 285
J. M. M!611er, Extensions of p-compact groups ........................ 307
A. Nofech, A version of an E2 closed model category structure ....... 329
D. Notbohm, p-adic lattices of pseudo reflection groups ............... 337
E. Ossa, On the cohomology of configuration spaces ................... 353
A. Osse, On isomorphism classes of locally unitary groups 363
G. Peschke, Localization and genus in group theory and
homotopy theory ................................................ 381
Y. Xia, On the connectivity of posets in the mapping class group ..... 393
Foreword
The 1994 Barcelona Conference on Algebraic Topology (BCAT) was held from
June 1 to 7 in Sant Feliu de Gufxols, a small town on the Northern Catalan
coast. As in the previous meetings of the same series, the conference was orga
nized by the Centre de Recerca Matematica (CRM), a mathematical research
institute sponsored by the Institut d'Estudis Catalans. The 1994 BCAT was a
part of the activities which took place during a semester devoted to algebraic
topology at the CRM. The very stimulating atmosphere created by semester
visitors and conference participants is reflected in these proceedings. Some of
the articles were completed -or even born- in Barcelona during that period.
Articles were submitted between July and November 1994. We are deeply
indebted to the authors for their prompt and generous response to our invita
tion to send us their most recent work. Thus, the volume reports on current
progress in algebraic topology, focusing on advances in localization and peri
odicity in homotopy theory, as a central but not exclusive topic.
All articles have been thoroughly refereed. We take this opportunity to
thank the referees once more for their help in the selection of the articles, as
well as for their valuable contribution in the improvement of several of them.
The conference organizers were Jaume Aguade, Manuel Castellet, and
Guido Mislin. They join us in thanking the secretaries Consol Roca, Maria
Julia, and Sylvia Hoemke for their help before, during, and after the conference.
We extend our thanks to the Direcci6 General de Recerca de la Generalitat de
Catalunya and the Direcci6n General de Investigaci6n Cientffica y Tecnica for
their partial financial support. Finally, thanks are due to Birkhiiuser Verlag
for their interest in the publication of this volume.
Carles Broto
Carles Casacuberta
Guido Mislin
Bellaterra, April 1995
List of participants
J. Aguade C. Elvira
J. Amoros M.1. GaJvez
M. Arkowitz H. H. Glover
D. Arlettaz M. Golasiriski
G. Arone M. Grandis
M. Bendersky V. Halperin
D. Blanc M. Hartl
A. K. Bousfield A. Hatcher
C. Broto F. Hegenbarth
M. Brunetti J. R. Hubbuck
R. Budney N. H. V. Hu'ng
J. Cabeza J. R. Hunton
H. E. A. Campbell P.Igodt
C. Casacuberta 1. M. James
M. Castellet A. Jeanneret
A. Cavicchioli R. Kane
B. Cenkl M. Kankaanrinta
W. ChachOlski T. Kashiwabara
D. Christensen L. Langsetmo
F. R. Cohen 1. J. Leary
J. A. Crespo K. Lesh
M. Crossley R. Levi
J. Cruickshank 1. Llerena
W. Dreckmann L. Lomonaco
E. Dror Farjoun M. Mahowald
W. G. Dwyer J. Martino
List of Participants ix
C. A. McGibbon Y. Rudyak
H. R. Miller J. W. Rutter
G. Mislin M. Santos
J. M. M0ller L. Saumell
A. Murillo D. Scevencls
J. L. Navarro B. Schuster
J. Neisendorfer R. Shank
F. Neumann B. Shipley
M. Neusel L. Smith
A. Nofech S. Smith
D. Notbohm D. Tamaki
E. Ossa M. Tanabe
A.Osse P. Turner
G. Peschke V. V. Vershinin
M. Pfenniger A. Virucl
S. B. Priddy Y. Xia
D. Randall K. Xu
D. C. Ravenel S. Zarati
J. 1. Rodriguez P. Zhang