Description 
1 online resource : illustrations 
Series 
Nankai tracts in mathematics ; v. 12 

Nankai tracts in mathematics ; v. 12.

Contents 
Foreword; Preface; Short Biography of Lin; Mathematics of Lin; Organizing Committees; List of Participants; Program; Welcome Speech of Weiping Zhang; Speech of Boju Jiang; CONTENTS; Part A Invited Contributions; The Modified CalabiYau Problems for CRmanifolds J. Cao and S.C. Chang; 0. Introduction; 1. Bounded solutions to d = on manifolds with negative curvature; 2. The modified CalabiYau problems for singular spaces and CRmanifolds; A. Supharmonic functions on Alexandrov spaces with nonnegative sectional curvature 

B. The generalized Calabi problems for Kahler domains with boundaries C. The CalabiEscobar type problem for Kahler domains with boundaries; Acknowledgments; References; On Picture (2+1)TQFTs M. Freedman, C. Nayak, K. Walker and Z. Wang; 1. Introduction; 2. Jones representations; 2.1. Braid statistics; 2.2. Generic Jones representation of the braid groups; 2.3. Unitary Jones representations; 2.4. Uniqueness of JonesWenzl projectors; 3. Diagram TQFTs for closed manifolds; 3.1. ""disotopy"", local relation, and skein relation; 3.2. Picture classes; 3.3. Skein classes; 3.4. Recoupling theory 

3.5. Handles and Smatrix 3.6. Diagram TQFTs for closed manifolds; 3.7. Boundary conditions for picture TQFTs; 3.8. JonesKauffman skein spaces; 4. Morita equivalence and cutpaste topology; 4.1. Bimodules over picture category; 4.2. Cutting and paste as Morita equivalence; 4.3. Annualization and quantum double; 5. TemperleyLiebJones categories; 5.1. Annular Markov trace; 5.2. Representation of TemperleyLiebJones categories; 5.3. Rectangular TempeleyLiebJones categories for low levels; 5.3.1. Level=1, d2 = 1; 5.3.2. Level=2, d2 = 2; 5.3.3. Level=3, d2 = 1 + d or d2 = 1 

5.4. Annular TemperleyLiebJones theories for low levels 5.4.1. Level=1, d2 = 1; 5.4.2. Level=2, d2 = 2; 5.4.3. Level=3, d2 = 1 + d or d2 = 1; 5.5. TemperleyLiebJones categories for primitive 4th roots of unity; 5.6. TemperleyLiebJones categories for primitive 2nd root of unity, rodd; 6. The definition of a TQFT; 6.1. Redined labels for TQFTs; 6.2. Anomaly of TQFTs and extended manifolds; 6.3. Axioms for TQFTs; 6.4. More consequences of the axioms; 6.5. Framed link invariants and modular representation; 6.6. Verlinde algebras and Verlinde formulas 

7. Diagram and JonesKau man TQFTs 7.1. Diagram TQFTs; 7.2. JonesKau man TQFTs; 8. WRT and TuraevViro SU(2)TQFTs; 8.1. Flagged TLJ categories; 8.2. TuraevViro Unitary TQFTs; 8.3. WRT Unitary TQFTs; 9. BlackWhite TQFTs; 9.1. Blackwhite TLJ categories; 9.2. Labels for blackwhite theories; 9.2.1. Level=2, d2 = 2; 9.2.2. Level=3; 9.3. BW TQFTs; 10. Classification and Unitarity; 10.1. Classification of diagram local relations; 10.2. Unitary TQFTs; 10.3. Classication and unitarity; Appendix A. Topological phases of matter; Ground states manifolds as modular functors 
Summary 
This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of XiaoSong Lin, presents a broad connection between topology and physics as exemplified by the relationship between lowdimensional topology and quantum field theory. The volume includes works on picture (2+1)TQFTs and their applications to quantum computing, Berry phase and YangBaxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, GromovWitten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flo 
Notes 
Title from PDF title page (viewed on Apr. 3, 2013) 

Papers from a memorial conference in honor of XiaoSong Lin, organized by the Chern Institute of Mathematics and held in Tianjin, July 2731, 2007 
Bibliography 
Includes bibliographical references 
Notes 
English 
Subject 
Lowdimensional topology  Congresses


Quantum field theory  Congresses


Algebraic topology  Congresses


Field theory (Physics)  Congresses


MATHEMATICS  Topology.


Algebraic topology


Field theory (Physics)


Lowdimensional topology


Quantum field theory

Genre/Form 
Conference papers and proceedings

Form 
Electronic book

Author 
Lin, Xiaosong, 19572007.


Lin, Kevin


Wang, Zhenghan.


Zhang, Weiping, 1964


Nankai International Conference in Memory of XiaoSong Lin (2007: Tianjin, China)

LC no. 
2008300880 
ISBN 
9789812819116 

9812819118 

9789812819109 

981281910X 
