CONTEMPORARY MATHEMATICS

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Geometric Topology Joint U.S. -Israel Workshop on Geometric Topology

June 10-161 1992 Technion I Haifa I Israel

Cameron Gordon Yoav Moriah

Bronislaw Wajnryb Editors

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http://dx.doi.org/10.1090/conm/164

CoNTEMPORARY MATHEMATICS

164

Geometric Topology Joint U.S.-Israel Workshop on Geometric Topology

June 10-16, 1992 Technion, Haifa, Israel

Cameron Gordon Yoav Moriah

Bronislaw Wajnryb Editors

American Mathematical Society Providence, Rhode Island

Geometric Topology

EDITORIAL BOARD Craig Huneke, managing editor

Clark Robinson J. T. Stafford Linda Preiss Rothschild Peter M. Winkler

The Joint U.S.-Israel Workshop on Geometric Topology was held June 10-16, 1992, at the Amado Mathematics Building, Technion, Haifa, Israel, with support provided by the Institute of Advanced Studies in Mathematics of the Technion and the U.S.-Israel Binational Science Foundation.

1991 Mathematics Subject Classification. Primary 57M05, 57M07, 57M25, 57M50, 57Q45, 57M60.

Library of Congress Cataloging-in-Publication Data Joint U.S.-Israel Workshop on Geometric Topology (1992: Haifa, Israel)

Geometric topology: Workshop on Geometric Topology, June 10-16, 1992, Technion, Haifa, Israel / [edited by] Cameron Gordon, Yoav Moriah, Bronislaw Wajnryb.

p. em. -(Contemporary mathematics; v. 164) ISBN 0-8218-5182-9 1. Low-dimensional topology-Congresses. I. Gordon, Cameron, 1945-. II. Moriah, Yoav,

1952-. Ill. Wajnryb, Bronislaw, 1946-. IV. Title. V. Series: Contemporary mathematics (American Mathematical Society); v. 164. QA612.14.W67 1992 514'.2-dc20

94-11696 CIP

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Contents

Introduction ix

List of Participants xi

The 3-torus is Kervaire ANDREW J. DUNCAN AND JAMES HOWIE 1

A topological interpretation of the Atiyah-Patodi-Singer invariant M. FARBER AND J. LEVINE 9

On groups of special NEC type-A Freiheitssatz and related results for a class of multi-relator groups

BENJAMIN FINE AND GERHARD ROSENBERGER 17

Collapsing and reconstruction of manifolds DAVID GILLMAN, SERGEI MATVEEV, AND DALE ROLFSEN 35

Metrics on manifolds with convex or concave boundary JOEL HASS 41

Geometric structures on brancqed covers over universal links KERRY N. JONES 47

Link homotopy and skein modules of 3-manifolds U~K~~ W

Bordism of link maps and selfintersections ULRICH KOSCHORKE 79

The monodromy of the Brieskorn bundle A. LEIBMAN AND D. MARKUSHEVICH 91

Verlinde formulae for surfaces with spin structure G. MASBAUM AND P. VOGEL 119

Knots that cannot be obtained from a trivial knot by twisting KATURA MIYAZAKI AND AKIRA YASUHARA 139

The arithmetic of braids and a statement of Chisini B. MOISHEZON 151

vii

viii CONTENTS

On tunnel number and connected sum of knots and links KANJI MORIMOTO 177

Essential laminations in 3-manifolds obtained by surgery on 2-bridge knots RAMIN N AIMI 183

A dynamical system approach to free actions on IR-trees: A survey with com-plements

FREDERIC PAULIN 187

On a tangle presentation of the mapping class groups of surfaces SERGEI MATVEEV AND MICHAEL POLYAK 219

Thin position for 3-manifolds MARTIN SCHARLEMANN AND ABIGAIL THOMPSON 231

On embeddings of a graph into R 3

KOUKI TANIYAMA 239

Introduction

Geometric topology is an area of topology that has gone through tremendous changes in the last decade or so. In fact a lot of the big questions and problems that were facing mathematicians in the area have been answered, and new directions and problems have arisen. One of the characteristics of geometric topology is that the techniques that are used in the area are very diverse. The purpose of the conference was to bring people working in the different subareas to "touch base" and to learn what other people were doing.

These proceedings contain refereed reports from eighteen lectures given at the conference. Altogether sixty-two people registered for the conference. Our guests included mathematicians from all over the world: 25 from the U.S.A., 17 from Israel, 7 from France, 5 from Japan, 3 from Germany, 2 from the U.K., and 1 each from Canada, China, and Mexico.

The organizers wish to thank the sponsors of the conference, which were the Institute of Advanced Studies in Mathematics of the Technion and the U.S.-Israel Binational Science Foundation. We would also like to thank Sylvia Shur and Hava Harel of the Faculty of Mathematics of the Technion for the outstanding job they did before and during the conference.

Finally, we remember our colleague and outstanding mathematician Professor Boris Moishezon, who passed away unexpectedly in August 1993.

Haifa, October 1993

ix

Cameron Gordon Yoav Moriah

Bronek Wajnryb

List of Participants

Dr. E. Appelbaum, Department of Mathematics, Technion-Israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor L. Birbrair, Kiryat Arba 7/9, 90100 Jerusalem, Israel.

Professor J. Birman, Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.

Dr. D. Blanc, Department of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.

Professor M. Boileau, Department of Mathematics, University Paul Sabatier, UER MIG, 118 Rte de Narbonne, 31062 Toulouse cedex, France.

Professor F. Bonahon, Department of Mathematics, University of Southern Cali-fornia, Los Angeles, CA 90089-1113, U.S.A.

Professor P. Callahan, Department of Mathematics, University of fllinois, Urbana, IL 61801, U.S.A.

Professor A. Casson, Department of Mathematics, University of California, Berke-ley, CA 94720, U.S.A.

Professor M. Domergue, Department of Mathematics, University of Provence, Case H, F13331 Marseille 3, France.

Professor Mario Eudave-Munoz, Instituto de Matematicas, UNAM, Circuito Exte-rior, Ciudad Universitaria, Mexico D.F. 04510, Mexico.

Professor M. Farber, Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel.

Professor E. Flapan, Department of Mathematics, Pomona College, Claremont, CA 91711, U.S.A.

Professor D. Gabai, Department of Mathematics, Caltech, Pasedena, CA 91125, U.S.A.

Professor Rita Gitick, Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Professor V. Goldstein, Department of Mathematics, Ben Gurian University of the Negev, P.O. Box 653, 84105 Beersheva, Israel.

xi

xii LIST OF PARTICIPANTS

Professor C. Gordon, Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.

Dr. M. Grossberg, Department of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.

Professor J. Hass, Department of Mathematics, University of California, Davis, CA 95616, U.S.A.

Professor Andrew Duncan, Department of Mathematics, Heriot- Watt University, Riccarton, Edinburgh EH14 4AS, Scotland, U.K.

Professor A. Juhasz, Department of Mathematics, Technion-israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor Uwe Kaiser, Department of Mathematics, Brandeis University, Waltham, MA 02254, U.S.A.

Professor 0. Kakimizu, Department of Education, Igarashi-Nino Machi, Migata-shi 950-21, Japan.

Professor E. Kalfagianni, Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.

Professor C. Kearton, Department of Mathematics, Durham University, Durham, DH1 3LE, England.

Professor M. Kidwell, U.S. Naval Academy, Chauvenet Hall, Annapolis, MD 21402-5002, U.S.A.

Professor U. Koschorke, Mathematics Institute, University of Siegen, FB6, Holder-linst 3, 59 Siegen 21, Germany.

Professor C. Lescop, Ecole Normale Superieure de Lyon, 46 Allee d'Italie, 69364 Lyon cedex 07, France.

Professor K. Jones, Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A.

Professor A. Lubotzky, Department of Mathematics, Hebrew University of Jeru-salem, 91904 Jerusalem, Israel.

Professor D. Markushevich, Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel.

Professor Yoshihiko Marumoto, Department of Mathematics, Osaka Sangyo Uni-versity, Nakagaito 3-1-1, Daito, Osaka 574, Japan.

Professor Y. Mathieu, Department of Mathematics, University of Provence, Case H, F13331 Marseille 3, France.

Professor W. Menasco, Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14214, U.S.A.

Professor K. Miyazaki, Department of Mathematics, Tsuda College, Tsuda-Machi Kodaira-shi, Tokyo 187, Japan.

LIST OF PARTICIPANTS xiii

Professor B. Moishezon, Department of Mathematics, Hebrew University of Jeru-salem, 91904 Jerusalem, Israel.

Dr. Yoav Moriah, Department of Mathematics, Technion-Israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor J. Levine, Department of Mathematics, Brandeis University, Waltham, MA 02254, U.S.A.

Professor V. Lin, Department of Mathematics, Technion-Israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor F. Paulin, Department of Mathematics, Ecole Normale Super de Lyon, 46 Allee d'Italie, 69364 Lyon 07 cedex, France.

Dr. V. Polterovitch, Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel.

Professor Michael Polyak, School of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel.

Dr. Yoav Rieck, Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.

Professor D. Rolfsen, Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Y4, Canada.

Professor G. Rosenberger, Fach Math., University of Dortmund, Postfach 50 05 00, D-4600, Germany.

Dr. Emil Saucan, Department of Mathematics, Technion-Israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor K. Morimoto, Department of Mathematics, Takushoku University, Tate-mochi, Hachigi, Tokyo 193, Japan.

Dr. Ramin Naimi, Department of Mathematics, Technion-Israel Institute of Tech-nology, 32000 Haifa, Israel.

Professor P. Shalen, Department of Mathematics, University of fllinois at Chicago, Chicago, IL 60680, U.S.A.

Dr. Yafim Schwartzman, Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel.

Professor K. Taniyama, Department of Mathematics, School of Education, Waseda University, Shinjuku, Tokyo, Japan.

Professor A. Thompson, Department of Mathematics, University of California, Davis, CA 95616, U.S.A.

Professor V. Touraev, Department of Mathematics, University Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg, France.

Professor J. Viro, Dept. of Mathematics f3 Computer Science, University of Cali-fornia, Riverside, CA 95521, U.S.A.

xiv LIST OF PARTICIPANTS

Professor 0. Viro, Dept. of Mathematics & Computer Science, University of Cali-fornia, Riverside, CA 95521, U.S.A.

Professor M. Scharlemann, Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.

Professor P. Scott, Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Dr. Zlil Sela, Department of Mathematics, Princeton University, Princeton, NJ 08544, U.S.A.

Professor P. Vogel, Department of Mathematics, University of Paris VII, 2 Place Jussiev, Paris F75251, France.

Professor B. Wajnryb, Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel.

ProfessorS. Wang, Department of Mathematics, Beijing University, Beijing China.

Dr. E. Weinstein, Department of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.

Dr. D. Yavin, Max-Planck-Institut fur Mathematik, Gottfried-Claren Str. 26, 5300 Bonn 3, Germany.

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(See the AMS catalog for earlier titles)

Geometric Topology Cameron Gordon, Y oav Moriah, and Bronislaw Wajnryb, Editors

Geometric topology has undergone tremendous changes in the past decade or so. Many of the big questions facing mathematicians in this area have been answered, and new directions and problems have arisen. One of the characteris-tics of the field is the diversity of tools researchers bring to it. The Workshop on Geometric Topology was held in June 1992 at Technion-Israel Institute of Tech-nology in Haifa, to bring together researchers from different subfields to share knowledge, ideas, and tools. This volume contains the refereed proceedings of the conference.

ISBN 0-8218-5182-9

9 780821 851821