Topology And Physics - Proceedings Of The Nankai International Conference In Memory Of Xiao-song Lin

by Zhenghan Wang (Editor), Weiping Zhang (Editor), Kelvin Lin (Editor)

Overview

This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang-Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov-Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi-Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.

Product Details

ISBN-13:	9789812819109
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	08/12/2008
Series:	Nankai Tracts In Mathematics , #12
Pages:	468
Product dimensions:	6.20(w) x 9.00(h) x 1.20(d)

Table of Contents

Foreword ix

Preface xi

Short Biography of Lin xiii

Mathematics of Lin xv

Organizing Committees xviii

List of Participants xx

Program xxii

Welcome Speech of Weiping Zhang xxv

Speech of Boju Jiang xxvii

Part A Invited Contributions 1

The Modified Calabi-Yau Problems for CR-manifolds J. Cao S.-C. Chang 3

On Picture (2+1)-TQFTs M. Freedman C. Nayak K. Walker Z. Wang 19

Berry Phase in Yang-Baxter Approach Related to Entangled States and the Yang-Baxterization of Braid Relation for Two-state Anyon Model M.-L. Ge L. Kauffman K. Xue 107

On a Conjecture of Milnor about Volume of Simplexes R. Guo F. Luo 122

On the Classification of Links up to Finite Type N. Habegger J.B. Meilhan 138

Generalized Ricci Flow I: Local Existence and Uniqueness C.-L. He S. Hu D.-X. Kong K. Liu 151

Unitary Representations of the Artin Braid Groups and Quantum Algorithms for Colored Jones Polynomials and the Witten-Reshetikhin Invariant L. H. Kauffman S. J. Lomonaco Jr. 172

A New Approach to Deriving Recursion Relations for the Gromov-Witten Theory Y.-S. Kim K. Liu 195

Link Groups and the A-B Slice Problem V.-S. Krushkal 220

Twisted L[superscript 2]-Alexander-Conway Invariants for Knots W. Li W. Zhang 236

Existence of Knots of Minimum Energy and Topological Growth Laws in the Faddeev Model F. Lin Y. Yang 260

On Translation Invariant Symmetric Polynomials and Haldane's Conjecture J. Liptrap 279

Additional Gradings in Khovanov Homology V.O. Manturov 288

Towards the Large N Duality between the Chern-Simons Gauge Theory and the Topological String Theory P. Peng 326

On the Heegaard Genera of 3-manifolds Containing Non-separating Surfaces R. Qiu F. Lei 341

A GeometricCategorification of Representations of U[subscript q](sl[subscript 2]) H. Zheng 348

Part B Xiao-Song Lin's Unpublished Papers 357

Editors' Notes 359

Markov Theorems for Links in 3-Manifolds 360

Vertex Models, Quantum Groups, and Vassiliev's Knot Invariants 370

Knot Invariants and Iterated Integrals 384

Invariants of Legendrian Knots 395

The Motion Group of the Unlink and its Representations 411

Part C Lin Award, Speeches and Writings 419

Lin Award Information 421

Selected Speeches at the Funeral 423

Freedman's Writings on Lin 430

Jian-Pin He's Speech 432