LEADER 05092nam 2200745 450 001 9910796663203321 005 20230808202709.0 010 $a3-11-043456-3 010 $a3-11-043522-5 024 7 $a10.1515/9783110435221 035 $a(CKB)3850000000001078 035 $a(EBL)4595505 035 $a(SSID)ssj0001693427 035 $a(PQKBManifestationID)16546613 035 $a(PQKBTitleCode)TC0001693427 035 $a(PQKBWorkID)15065037 035 $a(PQKB)25091906 035 $a(MiAaPQ)EBC4595505 035 $a(DE-B1597)456467 035 $a(OCoLC)958054778 035 $a(OCoLC)990671256 035 $a(DE-B1597)9783110435221 035 $a(Au-PeEL)EBL4595505 035 $a(CaPaEBR)ebr11237002 035 $a(CaONFJC)MIL941040 035 $a(OCoLC)954046710 035 $a(EXLCZ)993850000000001078 100 $a20160814h20162016 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum invariants of knots and 3-manifolds /$fVladimir G. Touraev 205 $aThird edition. 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cWalter de Gruyter GmbH,$d2016. 210 4$dİ2016 215 $a1 online resource (608 p.) 225 1 $ade Gruyter Studies in Mathematics,$x0179-0986 ;$v18 300 $aDescription based upon print version of record. 311 $a3-11-044266-3 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction -- $tPart I. Towards Topological Field Theory -- $tChapter I. Invariants of graphs in Euclidean 3-space -- $tChapter II. Invariants of closed 3-manifolds -- $tChapter III. Foundations of topological quantum field theory -- $tChapter IV. Three-dimensional topological quantum field theory -- $tChapter V. Two-dimensional modular functors -- $tPart II. The Shadow World -- $tChapter VI. 6j-symbols -- $tChapter VII. Simplicial state sums on 3-manifolds -- $tChapter VIII. Generalities on shadows -- $tChapter IX. Shadows of manifolds -- $tChapter X. State sums on shadows -- $tPart III. Towards Modular Categories -- $tChapter XI. An algebraic construction of modular categories -- $tChapter XII. A geometric construction of modular categories -- $tAppendix I. Dimension and trace re-examined -- $tAppendix II. Vertex models on link diagrams -- $tAppendix III. Gluing re-examined -- $tAppendix IV. The signature of closed 4-manifolds from a state sum -- $tReferences -- $tSubject index 330 $aDue to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories 410 0$aDe Gruyter studies in mathematics ;$v18. 606 $aQuantum field theory 606 $aKnot theory 606 $aThree-manifolds (Topology) 606 $aInvariants 606 $aMathematical physics 615 0$aQuantum field theory. 615 0$aKnot theory. 615 0$aThree-manifolds (Topology) 615 0$aInvariants. 615 0$aMathematical physics. 676 $a514/.2242 686 $aSK 340$qSEPA$2rvk 700 $aTuraev$b V. G$g(Vladimir G.),$f1954-$067205 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910796663203321 996 $aQuantum invariants of knots and 3-manifolds$91106738 997 $aUNINA