Contemporary Mathematics 258

CONTEMPORARY MATHEMATICS 258

Geometry and Topology: Aarhus

Conference on Geometry and Topology August 10-16, 1998 Aarhus University Aarhus, Denmark

Karsten Grove lb Henning Madsen Erik Kjcer Pedersen Editors http://dx.doi.org/10.1090/conm/258

Selected Titles in This Series

258 Karsten Grove, Ib Henning Madsen, and Erik Kjaer Pedersen, Editors, Geometry and topology: Aarhus, 2000 257 Peter A. Cholak, Steffen Lempp, Manuel Lerman, and Richard A. Shore, Editors, Computability theory and its applications: Current trends and open problems, 2000 256 Irwin Kra and Bernard Maskit, Editors, In the tradition of Ahlfors and Bers: Proceedings of the first Ahlfors-Bers colloquium, 2000 255 Jerry Bona, Katarzyna Saxton, and Ralph Saxton, Editors, Nonlinear POE's, dynamics and continuum physics, 2000 254 Mourad E. H. Ismail and Dennis W. Stanton, Editors, q-series from a contemporary perspective, 2000 253 Charles N. Delzell and James J. Madden, Editors, Real algebraic geometry and ordered structures, 2000 252 Nathaniel Dean, Cassandra M. McZeal, and Pamela J. Williams, Editors, African Americans in Mathematics II, 1999 251 Eric L. Grinberg, Shiferaw Berhanu, Marvin I. Knopp, Gerardo A. Mendoza, and Eric Todd Quinto, Editors, Analysis, geometry, number theory: The Mathematics of Leon Ehrenpreis, 2000 250 Robert H. Gilman, Editor, Groups, languages and geometry, 1999 249 Myung-Hwan Kim, JohnS. Hsia, Yoshiyuki Kitaoka, and Rainer Schulze-Pillot, Editors, Integral quadratic forms and lattices, 1999 248 Naihuan Jing and Kailash C. Misra, Editors, Recent developments in quantum affine algebras and related topics, 1999 247 Lawrence Wasson Baggett and David Royal Larson, Editors, The functional and harmonic analysis of wavelets and frames, 1999 246 Marcy Barge and Krystyna Kuperberg, Editors, Geometry and topology in dynamics, 1999 245 Michael D. Fried, Editor, Applications of curves over finite fields, 1999 244 Leovigildo Alonso Tarrio, Ana Jeremias Lopez, and Joseph Lipman, Studies in duality on noetherian formal schemes and non-noetherian ordinary schemes, 1999 243 Tsit Yuan Lam and Andy R. Magid, Editors, Algebra, K-theory, groups, and education, 1999 242 Bernheim Booss-Bavnbek and Krzysztof Wojciechowski, Editors, Geometric aspects of partial differential equations, 1999 241 Piotr Pragacz, Michal Szurek, and Jaroslaw Wisniewski, Editors, Algebraic geometry: Hirzebruch 70, 1999 240 Angel Carocca, Victor Gonzalez-Aguilera, and Rubi E. Rodriguez, Editors, Complex geometry of groups, 1999 239 Jean-Pierre Meyer, Jack Morava, and W. Stephen Wilson, Editors, Homotopy invariant algebraic structures, 1999 238 Gui-Qiang Chen and Emmanuele DiBenedetto, Editors, Nonlinear partial differential equations, 1999 237 Thomas Branson, Editor, Spectral problems in geometry and arithmetic, 1999 236 Bruce C. Berndt and Fritz Gesztesy, Editors, Continued fractions: From analytic number theory to constructive approximation, 1999 235 Walter A. Carnielli and Itala M. L. D'Ottaviano, Editors, Advances in contemporary logic and computer science, 1999 234 Theodore P. Hill and Christian Houdre, Editors, Advances in stochastic inequalities, 1999 233 Hanna Nencka, Editor, Low dimensional topology, 1999 (Continued in the back of this publication) Geometry and Topology: Aarhus CoNTEMPORARY MATHEMATICS

258

Geometry and Topology: Aarhus

Conference on Geometry and Topology August 1Q-16, 1998 Aarhus University Aarhus, Denmark

Karsten Grove lb Henning Madsen Erik Kjcer Pedersen Editors

American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor Andreas Blass Andy R. Magid Michael Vogelius

The fifth in a series of "Topology" conferences hosted by Aarhus University in connection with the ICM was held at Aarhus University, Aarhus, Denmark on August 1Q-16, 1998.

2000 Mathematics Subject Classification. Primary 53-XX, 55-XX, 57-XX.

Library of Congress Cataloging-in-Publication Data Geometry and topology, Aarhus : conference on geometry and topology, August 1G-16, 1998 Aarhus University Aarhus, Denmark/ Karsten Grove, Ib Henning Madsen, Erik Kjrer Pedersen, editors. p. em. -{Contemporary mathematics, ISSN 0271-4132 ; 258) Includes bibliographical references. ISBN 0-8218-2158-X {alk. paper) 1. Geometry-Congresses. 2. Topology-Congresses. I. Grove, Karsten. II. Madsen. I. H. (Ib Henning), 1942- Ill. Pedersen, Erik Kjrer, 1946- IV. Contemporary mathematics (Ameri- can Mathematical Society) ; v. 258. QA440 .G4695 1998 516--dc21 00-038943

Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- mt!mt of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permissionCiams. org. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) © 2000 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. § The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http: I /www. ams. org/ 10 9 8 7 6 5 4 3 2 1 05 04 03 02 01 00 Contents

Complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups A. BAKER AND c. OZEL 1 Unique continuation property for Dirac operators, revisited BERNHELM BOOSS-BAVNBEK 21 Torus actions determined by simple polytopes VICTOR M. BUCHSTABER AND TARAS E. PANOV 33 The Torelli group action on representation spaces S. E. CAPPELL, R. LEE, AND E. Y. MILLER 47 Notes on Seiberg-Witten-Floer theory ALAN L. CAREY AND BAI-LING WANG 71 Stability for holomorphic spheres and Morse theory RALPH L. COHEN, JOHN D. S. JONES, AND GRAEME B. SEGAL 87 Embedded minimal surfaces without area bounds in 3-manifolds TOBIAS H. GOLDING AND WILLIAM P. MINICOZZI II 107 The cyclotomic trace for symmetric monoidal categories BJ0RN IAN DUNDAS 121 Isoparametric submanifolds and symmetric spaces J.-H. ESCHENBURG 145 Obstructions to homotopy invariance in parametrized fixed point theory Ross GEOGHEGAN, ANDREW NicAs, AND DIRK ScHuTz 157 Lagrangian path intersections and the Leray index MAURICE DE GOSSON 177 Associativity in two-cell complexes BRAYTON GRAY 185 Nonnegative curvature and normal holonomy in open manifolds LUIS GUIJARRO 197 Compactifying infinite group actions IAN HAMBLETON AND ERIK K. PEDERSEN 203

vii viii CONTENTS

Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture MICHAEL JOACHIM AND THOMAS SCHICK 213 Stable modules and the structure of Poincare 3-complexes F. E. A. JOHNSON 227 The equivariant cohomology ring of the moduli space of vector bundles over a Riemann surface YOUNG-HOON KIEM 249 Poincare embeddings of spheres JOHN R. KLEIN 263 Beginning of analysis on Alexandrov spaces KAZUHIRO KUWAE, YOSHIROH MACHIGASHIRA, AND TAKASHI SHIOYA 275 Negative curvature and symplectic submanifolds JOACHIM LOHKAMP 285 On the universal space for group actions with compact isotropy WOLFGANG LUCK AND DAVID MEINTRUP 293 The circle transfer and K-theory lB MADSEN AND CHRISTIAN SCHLICHTKRULL 307 Finite groups possessing gap modules MASAHARU MORIMOTO, TOSHIO SUMI, AND MAMORU YANAGIHARA 329 Smith equivalence of group modules and the Laitinen conjecture. A survey KRZYSZTOF PAWALOWSKI 343 Controlled algebraic K-theory, a survey ERIK KJJER PEDERSEN 351 Taut codimension one spheres of odd order LAURENCE R. TAYLOR 369 Bivariant Riemann Roch Theorems BRUCE WILLIAMS 377 Preface

The 5th in a series of "Topology"- conferences hosted by Aarhus University in connection with the ICM, when located in Europe, was held August 10-16, 1998 at the Mathematics Institute. The tradition started in 1962 with a conference on "Algebraic Topology", but over the years, the emphasis has moved more towards manifold theory and geometry. The conference was supported by the Danish Nat- ural Research Council and by a special grant from Aarhus University. The meeting was structured with plenary lectures in the morning together with three parallel special sessions in the afternoon. In addition, posters were exhibited throughout the conference. Complete lists of participants and their affiliation is given starting on page xi. These proceedings contain papers which were presented at the conference, and some related papers. There is a mix of research and survey articles. All papers have been refereed and we take this opportunity to thank the many referees. We would like to thank everyone who contributed to the success of the conference. In particular we thank the City of Aarhus for inviting all participants and their companions to a soupe in the Town Hall. We also acknowledge the help provided by the Aarhus Congress Bureau for arranging accomodations. Special thanks go to Karina Thorup Nielsen and Sanna Vejlin Nielsen who handled the administrative and secretarial duties. lb Madsen, Karsten Grove, and Erik Kjrer Pedersen

ix List of Participants

Bedia Akyar University of Aarhus Levan Alania Moscow State University J0rgen Ellegaard Andersen University of Aarhus Laura Anderson Texas A&M University Pawel Andrezejewskii Uniwersytet Szczecinski C. S. Aravinda SPIC Mathematical Institute Niels A.Baas Norwegian Technical University Andrew Baker University of Glasgow Markus Banagl Courant Institute Steffen Bentzen University of Aarhus Terrence Bisson .Canisius College Dorota Blachowska University of Lodz Konrad Blachowski University of Lodz Bernheim Booss-Bavnbek University of Roskilde Raoul Bott Harvard University William Browder Princeton University Morten Brun University of Oslo Rogier Brussee University of Bielefeld Ulrich Bunke University of Gttingen Marcel Bokstedt University of Aarhus Sylvain Cappell Courant Institute Gunnar Carlsson Stanford University Minshik Cho Korea National University of Education Ralph Cohen Stanford University Tobias Colding Courant Institute Dario Pasquale Coluzzi University of Rome Frank Connolly University of Notre Dame Octavian Cornea University of Lille 1 James Davis Indiana University Wojciech Dorabiala University of Notre Dame Bj0rn Dundas Norwegian Technical University Johan Dupont University of Aarhus Robert Edwards UC at Los Angeles Tobias Ekholm University of Uppsala Yakov Eliashberg Stanford University Jost-Hinrich Eschenburg University of Augsburg

xi xii LIST OF PARTICIPANTS

Lisbeth Fajstrup University of Aalborg Tom Farrell Binghamton University Ron Fintushel Michigan State U niversiy Ross Geoghegan Binghamton University Vassily Gorbuounov University of Kentucky Maurice de Gosson University of Karlskrona-Ronneby Daniel Gottlieb Purdue University Brayton Gray University of Illinois at Chicago Ralph Grieder Northwestern University Ursula Gritsch University of Cambridge Jakob Grove University of Aarhus Karsten Grove University of Maryland Luis Guijarro University of Pennsylvania Ian Hambleton McMaster University S0ren Kold Hansen University of Aarhus Jean-Claude Hausmann University of Geneva Friedrich Hegenbarth University of Milan Lars Hesselholt Princeton University Jonathan A. Hillman University of Sydney Helmuth Hofer Courant Institut Ilkka Holopainen University of Helsinki Michael Hopkins MIT Wu-chung Hsiang Princeton University Jacques Hurtubise McGill University Thomas Huttemann University of Bielefeld Stefan Jackowski University of Warsaw Bj0rn Jahren University of Oslo Myung-Jin Jeon Semyung University Michael Joachim University of Munster Francis E. A. Johnson University College of London Heather Johnston Rutgers University John Jones Universtity of Warwick Maria Helena Jorge Courant Institute Franz W. Kamber University of Illinois George Khimshiashvili University of Lodz John R. Klein University of Bielefeld Katarzyna Kozuch University of Wroclaw Leif Kristensen University of Aarhus Jens Christian Larsen The Royal Veterinary and Agricultural University Ronnie Lee Yale University Jerry Lodder New Mexico State University Joachim Lohkamp University of Augsburg Wolfgang Luck University o Munster Ib Madsen University of Aarhus Mark Mahowald Northwestern University Vladimir Manuilov Moscow State University Wolfgang Meyer University of Munster LIST OF PARTICIPANTS xiii

Jim Milgram Stanford University Masaharu Morimoto University of Okayama Jesper M¢ller University of Copenhagen Alexander N abutovsky University of Toronto Kre Nielsen University of Aarhus Bob Oliver University of Paris Nord Olop-Petter Ostlund University of Uppsala Iver Ottesen University of Oslo Taras Panov Moscow State University Doug Park Princeton University Krzysztof Pawalowski University of Poznan Erik Kjrer Pedersen Binghamton University Kirsi Peltonen Helsinki University of Technology Andrew du Plessis University of Aarhus Efstratios Prassidis Vanderbilt University Carlos Prieto UNAM Volker Puppe University of Konstanz Frank Quinn Virginia Tech Andrew Ranicki University of Edingburgh Martin Raussen University of Aalborg Charles Rezk Northwestern University Rosaria Rota University of Rome Melvin Rothenberg University of Chicago Regina Rotman University of Toronto James Schafer University of Maryland Thomas Schick University of Munster Marco Schlichting University of Paris 7 Christian Schlichtkrull University of Aarhus Reinhard Schultz UC Riverside Julius Shaneson University of Pennsylvania Desmond Sheiham University of Edinburgh Takashi Shioya Kyushu University Christina Sormani John Hopkins University Christopher Stark National Science Foundation; USA Zoltan Szabo Princeton University Susan Szczepanski Lehigh University Kim Taesoon Mokwon University Hirotaka Tamanoi UC at Santa Cruz Laurence Tayler University of Notre Dame Gudlaugur Thorbergsson University of Kln Ulrike Tillmann University of Oxford Vladimir Thraev University of Strasbourg J0rgen Tornehave University of Aarhus Christina T0nnesen-Friedman University of Aarhus Henrik Vosegaard University of Aarhus Jack Wagoner UC Berkeley Bai-ling Wang University of Adelaide Charles Weibel Rutgers University xiv LIST OF PARTICIPANTS

Dariusz Wilczynski Utah State University Burkhard Wilking University of Munster Bruce Williams University of Notre Dame Takao Yamaguchi Kyushu University Tsuneyo Yamanoshita Musashi Insitute of Technology Masayuki Yamasaki University of Josai MinYan Hong Kong University Selected Titles in This Series (Continued from the front of this publication)

232 Krzysztof Jarosz, Editor, Function spaces, 1999 231 Michael Farber, Wolfgang Liick, and Shmuel Weinberger, Editors, Tel Aviv topology conference: Rothenberg Festschrift, 1999 230 Ezra Getzler and Mikhail Kapranov, Editors, Higher category theory, 1998 229 Edward L. Green and Birge Huisgen-Zimmermann, Editors, Trends in the representation theory of finite dimensional algebras, 1998 228 Liming Ge, Huaxin Lin, Zhong-Jin Ruan, Dianzhou Zhang, and Shuang Zhang, Editors, Operator algebras and operator theory, 1999 227 John McCleary, Editor, Higher homotopy structures in topology and mathematical physics, 1999 226 Luis A. Caffarelli and Mario Milman, Editors, Monge Ampere equation: Applications to geometry and optimization, 1999 225 Ronald C. Mullin and Gary L. Mullen, Editors, Finite fields: Theory, applications, and algorithms, 1999 224 Sang Geun Hahn, Hyo Chul Myung, and Efim Zelmanov, Editors, Recent progress in algebra, 1999 223 Bernard Chazelle, Jacob E. Goodman, and Richard Pollack, Editors, Advances in discrete and computational geometry, 1999 222 Kang-Tae Kim and Steven G. Krantz, Editors, Complex geometric analysis in Pohang, 1999 221 J. Robert Dorroh, Gisele Ruiz Goldstein, Jerome A. Goldstein, and Michael Mudi Tom, Editors, Applied analysis, 1999 220 Mark Mahowald and Stewart Priddy, Editors, Homotopy theory via algebraic geometry and group representations, 1998 219 Marc Henneaux, Joseph Krasil'shchik, and Alexandre Vinogradov, Editors, Secondary calculus and cohomological physics, 1998 218 Jan Mandel, Charbel Farhat, and Xiao-Chuan Cai, Editors, Domain decomposition methods 10, 1998 217 Eric Carlen, Evans M. Harrell, and Michael Loss, Editors, Advances in differential equations and mathematical physics, 1998 216 Akram Aldroubi and EnBing Lin, Editors, Wavelets, multiwavelets, and their applications, 1998 215 M. G. Nerurkar, D. P. Dokken, and D. B. Ellis, Editors, Topological dynamics and applications, 1998 214 Lewis A. Coburn and Marc A. Rieffel, Editors, Perspectives on quantization, 1998 213 Farhad Jafari, Barbara D. MacCluer, Carl C. Cowen, and A. Duane Porter, Editors, Studies on composition operators, 1998 212 E. Ramirez de Arellano, N. Salinas, M. V. Shapiro, and N. L. Vasilevski, Editors, Operator theory for complex and hypercomplex analysis, 1998 211 J6zef Dodziuk and Linda Keen, Editors, Lipa's legacy: Proceedings from the Bers Colloquium, 1997 210 V. Kumar Murty and Michel Waldschmidt, Editors, Number theory, 1998 209 Steven Cox and Irena Lasiecka, Editors, Optimization methods in partial differential equations, 1997 208 MichelL. Lapidus, Lawrence H. Harper, and Adolfo J. Rumbos, Editors, Harmonic analysis and nonlinear differential equations: A volume in honor of Victor L. Shapiro, 1997

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