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Contemporary Mathematics 279 CONTEMPORARY MATHEMATICS 279 Topology/ Geometry/ and Algebra: Interactions and New Directions Conference on Algebraic Topology in Honor of R. James Milgram August 17-21, 1999 Stanford University Alejandro Adem Gunnar Carlsson Rolph Cohen Editors http://dx.doi.org/10.1090/conm/279 CoNTEMPORARY MATHEMATICS 279 Topology, Geometry, and Algebra: Interactions and New Directions Conference on Algebraic Topology in Honor of R. James Milgram August 17-21, 1999 Stanford University Alejandro Adem Gunnar Carlsson Ralph Cohen Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeThrck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume contains the proceedings of a conference on "Topology, Geometry, and Algebra: Interactions and New Directions," which was held at Stanford University, August 17-21, 1999. 2000 Mathematics Subject Classification. Primary 55Pxx, 55Rxx, 55Txx, 55Uxx, 57Nxx, 57Rxx. Library of Congress Cataloging-in-Publication Data Conference on Algebraic Topology (1999 : Stanford, Calif.) Topology, geometry, and algebra : interactions and new directions : Conference on Algebraic Topology in honor of R. James Milgram, August 17-21, 1999, Stanford, California/ Alejandro Adem, Gunnar Carlsson, Ralph Cohen, editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; 279) Includes bibliographical references. ISBN 0-8218-2063-X (alk. paper) 1. Algebraic topology-Congresses. I. Milgram, R. James. II. Adem, Alejandro. III. Carls- son, G.(Gunnar), 1952- IV. Cohen, Ralph L., 1952- V. Title. VI. Contemporary mathematics (American Mathematical Society) ; v. 279. QA612 .A67 1999 514'.2--dc21 2001037329 CIP 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- ment 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-permissionQams. 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.) © 2001 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 06 05 04 03 02 01 Contents Preface vn On Jim Milgram's mathematical work GUNNAR CARLSSON 1 A renormalized Riemann-Roch formula and the Thorn isomorphism for the free loop space MATTHEW ANDO AND JACK MORAVA 11 The 1-line of the K-theory Bousfield-Kan spectral sequence for Spin(2n + 1) MARTIN BENDERSKY AND DONALD M. DAVIS 37 Homologically exotic free actions on products of sm WILLIAM BROWDER 57 Surgery formulae for analytical invariants of manifolds s. E. CAPPELL, R. LEE, AND E. Y. MILLER 73 On genus one mapping class groups, function spaces, and modular forms FREDERICK R. COHEN 103 Poincare duality and deformations of algebras BERNHARD HANKE 129 An analog of the May-Milgram Model for configurations with multiplicities 8ADOK KALLEL . 135 Configuration spaces and the topology of curves in projective space 8ADOK KALLEL 151 Quantum methods in algebraic topology MAX KAROUBI 177 Adiabatic limits and foliations KEFENG LIU AND WEIPING ZHANG 195 Legendrian links of topological unknots KLAUS MOHNKE 209 Algebraic Poincare cobordism ANDREW RANICKI 213 v PREFACE In August 1999 a meeting was held at Stanford University on the subject of "Topology, Geometry and Algebra: Interactions and New Directions". The goal of the conference was to bring together distinguished researchers from a variety of areas related to algebraic topology and its applications. The list of invited speakers included: Greg Arone, Sylvain Cappell, Jon Carlson, Fred Cohen, Jim Davis, Don Davis, Tom Goodwillie, Yakov Eliashberg, Tom Farrell, Mike Hopkins, Eleny Ionel, Ronnie Lee, Ib Madsen, Mark Mahowald, Bob Oliver, Peter Oszvath, John Rognes, Abigail Thompson, Ulrike Tillmann and Efim Zelmanov. A number of topics were covered in the lectures, including qomotopy theory, moduli spaces, group cohomology, manifold theory, algebraic K-theory, low dimen- sional topology, symplectic geometry, etc. Special emphasis was made on breadth and interactions between different areas. A large number of postdocs, graduate students and established mathematicians attended the lectures. This volume con- tains twelve refereed papers on a wide variety of topics reflecting the nature of the conference. The conference was partly held to celebrate Jim Milgram's sixtieth birthday and to recognize his enormous contributions to algebraic topology over the past 35 years. His powerful mathematics, deep insight and breadth of knowledge have been an inspiration to many of us, and it is a great pleasure for us to dedicate this volume to him. The first paper in this volume is an outline of Jim Milgram's main mathematical contributions. Acknowledgements: We would like to thank the National Science Foundation as well as Stanford University for their generous financial support. We would like to thank Willene Perez for her valuable help in organizing the conference, and Diane Reppert for her excellent technical assistance in assembling this volume. Alejandro Adem Gunnar Carlsson Ralph Cohen vii Topology, Geometry, and Algebra: Interactions and New Directions Alejandro Adem, Gunnar Carlsson, and Ralph Cohen, Editors This volume presents the proceedings from the conference on "Topology, Geometry, and Algebra: Interactions and New Directions" held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgery theory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas. ISBN 0-8218-2063-X 9 780821 820636 CONM/279 .
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