Algebraic and Geometric Topology Proceedings of a Conference held at
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1126 Algebraic and Geometric Topology Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6-13, 1983
Edited by A. Ranicki, N. Levitt and F. Quinn
Springer-Verlag Berlin Heidelberg New York Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann
1126 Algebraic and Geometric Topology Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6-13, 1983
Edited by A. Ranicki, N. Levitt and F. Quinn
Springer-Verlag Berlin Heidelberg New York Tokyo
Editors Andrew Ranicki Department of Mathematics, Edinburgh University James Clerk Maxwell Building, The King's Buildings Edinburgh EH9 3JZ, Scotland, U. K. Norman Levitt Department of Mathematics, Rutgers University New Brunswick, NJ 08903, USA Frank Quinn Department of Mathematics, Virginia Polytechnic Institute Blacksburg, VA 24061, USA
Mathematics Subject Classification (1980): 55-02,57-02 ISBN 3-540-15235-0 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-15235-0 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertunqsqesellschaft Wort', Munich.
© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
PREFACE This volume was conceived as the proceedings of a conference on surgery theory held at Rutgers University in July, 1983. The editors have taken the opportunity to considerably expand the subject matter. The articles in this volume present original research on a wide range of topics in modern topology. They include important new material on the algebraic K-theory of spaces (Waldhausen, Vogell), the algebraic obstructions to surgery and finiteness
(Cappell and
Shaneson, Milgram, Pedersen and Weibel, Ranicki, Sondow), geometric and chain complexes (Davis, Quinn, Smith, Weinberger), characteristic classes (Levitt), and
groups (Assadi and Vogel). A paper of J.Levine on homotopy spheres, written
in 1969
sequel to the classic work of Kervaire
and Milnor but never published,
is also included.
Andrew Ranicki Norman Levitt Frank Quinn November, 1984
TABLE OF CONTENTS A.Assadi and P.Vogel
Semi free finite group actions on compact manifolds
S.Cappell and J.Shaneson Torsion in L-groups J.Davis
22
Higher diagonal approximations and skeletons of K(n,l) 's
51
J.Levine
Lectures on groups of homotopy spheres
62
N.Levitt
Some remarks on local formulae for PI
96
J .Milgram
Evaluating the Swan finiteness
J.Milgram
obstruction for finite groups
127
The Cappell-Shaneson example
159
E.Pedersen and C.Weibel A nonconnective K-theory
166
F.Quinn
Geometric algebra
182
A.Ranicki
The algebraic theory of tors
