LEADER 05951nam 2200757Ia 450 001 9910454773603321 005 20200520144314.0 010 $a981-281-911-8 035 $a(CKB)1000000000767580 035 $a(EBL)1193158 035 $a(SSID)ssj0000520139 035 $a(PQKBManifestationID)12175393 035 $a(PQKBTitleCode)TC0000520139 035 $a(PQKBWorkID)10508247 035 $a(PQKB)11496967 035 $a(MiAaPQ)EBC1193158 035 $a(WSP)00001466 035 $a(Au-PeEL)EBL1193158 035 $a(CaPaEBR)ebr10688200 035 $a(CaONFJC)MIL491731 035 $a(OCoLC)835180286 035 $a(EXLCZ)991000000000767580 100 $a20081030d2008 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aTopology and physics$b[electronic resource] $eProceedings of the Nankai International Conference in Memory of Xiao-Song Lin, Tianjin, China, 27-31 July 2007 /$feditors, Kevin Lin, Zhenghan Wang, Weiping Zhang 210 $aHackensak, N.J. $cWorld Scientific$dc2008 215 $a1 online resource (468 p.) 225 0 $aNankai tracts in mathematics ;$vv. 12 300 $aPapers from a memorial conference in honor of Xiao-Song Lin, organized by the Chern Institue of Mathematics and held in Tianjin, July 27-31, 2007. 311 $a981-281-910-X 320 $aIncludes bibliographical references. 327 $aForeword; 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 Calabi-Yau Problems for CR-manifolds J. Cao and S.-C. Chang; 0. Introduction; 1. Bounded solutions to d = on manifolds with negative curvature; 2. The modified Calabi-Yau problems for singular spaces and CR-manifolds; A. Sup-harmonic functions on Alexandrov spaces with nonnegative sectional curvature 327 $aB. The generalized Calabi problems for Kahler domains with boundaries C. The Calabi-Escobar 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 Jones-Wenzl projectors; 3. Diagram TQFTs for closed manifolds; 3.1. ""d-isotopy"", local relation, and skein relation; 3.2. Picture classes; 3.3. Skein classes; 3.4. Recoupling theory 327 $a3.5. Handles and S-matrix 3.6. Diagram TQFTs for closed manifolds; 3.7. Boundary conditions for picture TQFTs; 3.8. Jones-Kauffman skein spaces; 4. Morita equivalence and cut-paste topology; 4.1. Bimodules over picture category; 4.2. Cutting and paste as Morita equivalence; 4.3. Annualization and quantum double; 5. Temperley-Lieb-Jones categories; 5.1. Annular Markov trace; 5.2. Representation of Temperley-Lieb-Jones categories; 5.3. Rectangular Tempeley-Lieb-Jones 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 = 1 327 $a5.4. Annular Temperley-Lieb-Jones 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. Temperley-Lieb-Jones categories for primitive 4th roots of unity; 5.6. Temperley-Lieb-Jones 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 327 $a7. Diagram and Jones-Kau man TQFTs 7.1. Diagram TQFTs; 7.2. Jones-Kau man TQFTs; 8. WRT and Turaev-Viro SU(2)-TQFTs; 8.1. Flagged TLJ categories; 8.2. Turaev-Viro Unitary TQFTs; 8.3. WRT Unitary TQFTs; 9. Black-White TQFTs; 9.1. Black-white TLJ categories; 9.2. Labels for black-white 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 327 $aElementary excitations as particles 330 $aThis unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang-Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov-Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flo 410 0$aNankai Tracts in Mathematics 606 $aLow-dimensional topology$vCongresses 606 $aQuantum field theory$vCongresses 606 $aAlgebraic topology$vCongresses 606 $aField theory (Physics)$vCongresses 608 $aElectronic books. 615 0$aLow-dimensional topology 615 0$aQuantum field theory 615 0$aAlgebraic topology 615 0$aField theory (Physics) 676 $a514.22 676 $a514/.22 701 $aLin$b Xiao-song$f1957-2007.$0934351 701 $aLin$b Kevin$0934352 701 $aWang$b Zhenghan$0477537 701 $aZhang$b Weiping$f1964-$0902627 712 12$aNankai International Conference in Memory of Xiao-Song Lin$f(2007 :$eTianjin, China) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454773603321 996 $aTopology and physics$92103530 997 $aUNINA