TOPOLOGY AND PHYSICS Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin NANKAI TRACTS IN MATHEMATICS Series Editors: Yiming Long and Weiping Zhang Chern Institute of Mathematics Published Vol. 1 Scissors Congruences, Group Homology and Characteristic Classes by J. L. Dupont Vol. 2 The Index Theorem and the Heat Equation Method by Y. L.Yu Vol. 3 Least Action Principle of Crystal Formation of Dense Packing Type and Kepler’s Conjecture by W. Y. Hsiang Vol. 4 Lectures on Chern–Weil Theory and Witten Deformations by W. P. Zhang Vol. 5 Contemporary Trends in Algebraic Geometry and Algebraic Topology edited by Shiing-Shen Chern, Lei Fu & Richard Hain Vol. 6 Riemann–Finsler Geometry by Shiing-Shen Chern & Zhongmin Shen Vol. 7 Iterated Integrals and Cycles on Algebraic Manifolds by Bruno Harris Vol. 8 Minimal Submanifolds and Related Topics by Yuanlong Xin Vol. 9 Introduction to Several Complex Variables: Three Methods of Several Complex Variables by Yum-Tong Siu et al. Vol. 10 Differential Geometry and Physics edited by Mo-Lin Ge & Weiping Zhang Vol. 11 Inspired by S S Chern edited by Phillip A. Griffiths Vol. 12 Topology and Physics edited by Kevin Lin, Zhenghan Wang & Weiping Zhang ZhangJi - Topology & Phys.pmd 2 7/4/2008, 2:02 PM Nankai Tracts in Mathematics - Vol. 12 TOPOLOGY AND PHYSICS Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin Tianjin, China 27 - 31 JUIY 2007 Editors Kevin Lin University of California at Berkeley, USA Zhenghan Wang Microsoft Research Station Q, USA Weiping Zhang Chern Institute of Mathematics, China yp World Scientific NEW JERSEY LONDON SINGAPORE BElJlNG SHANGHAI HONG KONG TAIPEI CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. TOPOLOGY AND PHYSICS Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-281-910-9 ISBN-10 981-281-910-X Printed in Singapore. ZhangJi - Topology & Phys.pmd 1 7/4/2008, 2:02 PM July2,2008 14:55 WSPC-ProceedingsTrimSize:9inx6in ws-proc9x6master v Dedicated to the memory of Professor Xiao-Song Lin July 27, 1957|Jan. 14, 2007 July2,2008 14:55 WSPC-ProceedingsTrimSize:9inx6in ws-proc9x6master TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk July2,2008 14:55 WSPC-ProceedingsTrimSize:9inx6in ws-proc9x6master vii Independence, confidence, and dignity! The most cherished is the light given off when we cross paths. Xiao-Song Lin Dec. 7, 2006 July2,2008 14:55 WSPC-ProceedingsTrimSize:9inx6in ws-proc9x6master TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk July2,2008 14:55 WSPC-ProceedingsTrimSize:9inx6in ws-proc9x6master ix FOREWORD This volume through its diversity re(cid:13)ects Lin’s journal-editing side. In addition to the mathematics he did he always read widely and with good taste in and around all the lovely terrain which neighbors on topology. Topology, in this way is a good subject for an eclectic. There is almost no domain from condensed matter physics to p-adic analysis that one cannot (cid:12)nd a topological excuse to study. Lin, the journal editor, did this. I hope hewould(cid:12)nd thisvolumeinterestingandthoughtfulenoughthathemight have put it together himself. Lin was, with Fred Hickling, one of my (cid:12)rst two graduate students. So he and I (cid:12)gured out the thesis advising process together. I needed a lot of help. I had had an unusual education and had missed some of the steps. To my great relief Lin seemed to know how it would go. He would talk to me about what I was working on, focus in on something that I was not understanding properly and then dig in. As with most great students the advisor has little to do with the thesis. Lin had a great idea, which he developed with Habegger, and is further expanded in this volume. The idea was very reductionist, he thought the subject of knots and links had beguninthewrongplace,asifphysicistshadtriedtosolveforH+ without 2 doing the hydrogen atom (cid:12)rst. His idea was to study \string links" : arcs in a ball with (cid:12)xed boundary conditions, rather than ordinary links in S3. First thing (cid:12)rst. Do the local problem before going global. It was a very sensible idea and amazing that knot theory had existed 100 years without this idea popping up. I think, 20 years later in 2008, this idea would be considered obvious. But this is a sign that Lin and a few like him exerted a systematic in(cid:13)uence: localizing and systematizing geometric topology. If you like making topology more like quantum (cid:12)eld theory. Quantum (cid:12)eld theory is another area where Lin was in the vanguard. The idea that some (but not all) classical link invariants are naturally de- scribed as coe(cid:14)cients of a perturbative expansion was sorted out between Bar-NatanandLinintheearly1990sleadingquicklytothetheoryof(cid:12)nite type invariants. It was a thrill for me to see how Lin took to the then new