LEADER 04269nam 2200793 a 450 001 9910792329203321 005 20230725023512.0 010 $a1-282-71603-4 010 $a9786612716034 010 $a3-11-022184-5 024 7 $a10.1515/9783110221848 035 $a(CKB)2670000000019195 035 $a(EBL)533668 035 $a(OCoLC)630543201 035 $a(SSID)ssj0000426530 035 $a(PQKBManifestationID)11307439 035 $a(PQKBTitleCode)TC0000426530 035 $a(PQKBWorkID)10393344 035 $a(PQKB)10219378 035 $a(MiAaPQ)EBC533668 035 $a(DE-B1597)37205 035 $a(OCoLC)650811823 035 $a(OCoLC)719451546 035 $a(DE-B1597)9783110221848 035 $a(Au-PeEL)EBL533668 035 $a(CaPaEBR)ebr10385987 035 $a(CaONFJC)MIL271603 035 $a(EXLCZ)992670000000019195 100 $a20100614d2010 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum invariants of knots and 3-manifolds$b[electronic resource] /$fVladimir G. Turaev 205 $a2nd rev. ed. 210 $aBerlin $cDe Gruyter$d2010 215 $a1 online resource (604 p.) 225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$v18 300 $aDescription based upon print version of record. 311 $a3-11-022183-7 320 $aIncludes bibliographical references (p. [571]-588) and index. 327 $apt. 1. Towards topological field theory -- pt. 2. The shadow world -- pt. 3. Towards modular categories. 330 $aDue to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. From the contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories 410 0$aDe Gruyter studies in mathematics ;$v18. 606 $aQuantum field theory 606 $aKnot theory 606 $aThree-manifolds (Topology) 606 $aInvariants 610 $a3-Manifold Invariants. 610 $aKnots. 610 $aMonoidal Categories. 610 $aState Sums. 610 $aTopogical Field Theory. 615 0$aQuantum field theory. 615 0$aKnot theory. 615 0$aThree-manifolds (Topology) 615 0$aInvariants. 676 $a514.2242 676 $a514.34 686 $aSK 320$2rvk 700 $aTuraev$b V. G$g(Vladimir G.),$f1954-$067205 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910792329203321 996 $aQuantum invariants of knots and 3-manifolds$91106738 997 $aUNINA