Topology and Physics: Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin, Tianjin, China 27-31 July 2007

466 Pages·2008·4.087 MB·English

by  Kevin Lin, Zhenghan Wang, Weiping Zhang

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
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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.
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ISBN-13 978-981-281-910-9
ISBN-10 981-281-910-X
Printed in Singapore.
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Dedicated to the memory of Professor Xiao-Song Lin
July 27, 1957|Jan. 14, 2007
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vii
Independence,
confidence,
and dignity!
The most
cherished is the
light given off
when we cross
paths.
Xiao-Song Lin
Dec. 7, 2006
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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