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

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)

http://dx.doi.org/10.1090/conm/258

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 connec-tion 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

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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 con-ference. 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 Levan Alania J0rgen Ellegaard Andersen Laura Anderson Pawel Andrezejewskii C. S. Aravinda Niels A.Baas Andrew Baker Markus Banagl Steffen Bentzen Terrence Bisson Dorota Blachowska Konrad Blachowski Bernheim Booss-Bavnbek Raoul Bott William Browder Morten Brun Rogier Brussee Ulrich Bunke Marcel Bokstedt Sylvain Cappell Gunnar Carlsson Minshik Cho Ralph Cohen Tobias Colding Dario Pasquale Coluzzi Frank Connolly Octavian Cornea James Davis Wojciech Dorabiala Bj0rn Dundas Johan Dupont Robert Edwards Tobias Ekholm Y akov Eliashberg Jost-Hinrich Eschenburg

University of Aarhus Moscow State University University of Aarhus Texas A&M University Uniwersytet Szczecinski SPIC Mathematical Institute Norwegian Technical University University of Glasgow Courant Institute University of Aarhus . Canisius College University of Lodz University of Lodz University of Roskilde Harvard University Princeton University University of Oslo University of Bielefeld University of Gttingen University of Aarhus Courant Institute Stanford University Korea National University of Education Stanford University Courant Institute University of Rome University of Notre Dame University of Lille 1 Indiana University University of Notre Dame Norwegian Technical University University of Aarhus UC at Los Angeles University of Uppsala Stanford University University of Augsburg

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xii

Lisbeth Fajstrup Tom Farrell Ron Fintushel Ross Geoghegan Vassily Gorbuounov Maurice de Gosson Daniel Gottlieb Brayton Gray Ralph Grieder Ursula Gritsch Jakob Grove Karsten Grove Luis Guijarro Ian Hambleton S0ren Kold Hansen Jean-Claude Hausmann Friedrich Hegenbarth Lars Hesselholt Jonathan A. Hillman Helmuth Hofer Ilkka Holopainen Michael Hopkins Wu-chung Hsiang Jacques Hurtubise Thomas Huttemann Stefan Jackowski Bj0rn Jahren Myung-Jin Jeon Michael Joachim Francis E. A. Johnson Heather Johnston John Jones Maria Helena Jorge Franz W. Kamber George Khimshiashvili John R. Klein Katarzyna Kozuch Leif Kristensen Jens Christian Larsen

Ronnie Lee Jerry Lodder Joachim Lohkamp Wolfgang Luck Ib Madsen Mark Mahowald Vladimir Manuilov Wolfgang Meyer

LIST OF PARTICIPANTS

University of Aalborg Binghamton University Michigan State U niversiy Binghamton University University of Kentucky University of Karlskrona-Ronneby Purdue University University of Illinois at Chicago Northwestern University University of Cambridge University of Aarhus University of Maryland University of Pennsylvania McMaster University University of Aarhus University of Geneva University of Milan Princeton University University of Sydney Courant Institut University of Helsinki MIT Princeton University McGill University University of Bielefeld University of Warsaw University of Oslo Semyung University University of Munster University College of London Rutgers University Universtity of Warwick Courant Institute University of Illinois University of Lodz University of Bielefeld University of Wroclaw University of Aarhus The Royal Veterinary and

Agricultural University Yale University New Mexico State University University of Augsburg University o Munster University of Aarhus Northwestern University Moscow State University University of Munster

LIST OF PARTICIPANTS

Jim Milgram Masaharu Morimoto Jesper M¢ller Alexander N abutovsky Kre Nielsen Bob Oliver Olop-Petter Ostlund Iver Ottesen Taras Panov Doug Park Krzysztof Pawalowski Erik Kjrer Pedersen Kirsi Peltonen Andrew du Plessis Efstratios Prassidis Carlos Prieto Volker Puppe Frank Quinn Andrew Ranicki Martin Raussen Charles Rezk Rosaria Rota Melvin Rothenberg Regina Rotman James Schafer Thomas Schick Marco Schlichting Christian Schlichtkrull Reinhard Schultz Julius Shaneson Desmond Sheiham Takashi Shioya Christina Sormani Christopher Stark Zoltan Szabo Susan Szczepanski Kim Taesoon Hirotaka Tamanoi Laurence Tayler Gudlaugur Thorbergsson Ulrike Tillmann Vladimir Thraev J0rgen Tornehave Christina T0nnesen-Friedman Henrik Vosegaard Jack Wagoner Bai-ling Wang Charles Weibel

Stanford University University of Okayama University of Copenhagen University of Toronto University of Aarhus University of Paris Nord University of Uppsala University of Oslo Moscow State University Princeton University University of Poznan Binghamton University Helsinki University of Technology University of Aarhus Vanderbilt University UNAM University of Konstanz Virginia Tech University of Edingburgh University of Aalborg Northwestern University University of Rome University of Chicago University of Toronto University of Maryland University of Munster University of Paris 7 University of Aarhus UC Riverside University of Pennsylvania University of Edinburgh Kyushu University John Hopkins University National Science Foundation; USA Princeton University Lehigh University Mokwon University UC at Santa Cruz University of Notre Dame University of Kln University of Oxford University of Strasbourg University of Aarhus University of Aarhus University of Aarhus UC Berkeley University of Adelaide Rutgers University

xiii

xiv

Dariusz Wilczynski Burkhard Wilking Bruce Williams Takao Yamaguchi Tsuneyo Yamanoshita Masayuki Yamasaki MinYan

LIST OF PARTICIPANTS

Utah State University University of Munster University of Notre Dame Kyushu University Musashi Insitute of Technology University of Josai 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

For a complete list of titles in this series, visit the AMS Bookstore at www.ams.org/bookstore/.

ISBN 0-8218-2158-X