LEADER 04607nam 22007935 450 001 9910144598203321 005 20250724093327.0 010 $a3-540-44625-7 024 7 $a10.1007/b82618 035 $a(CKB)1000000000233213 035 $a(SSID)ssj0000325259 035 $a(PQKBManifestationID)12116390 035 $a(PQKBTitleCode)TC0000325259 035 $a(PQKBWorkID)10321702 035 $a(PQKB)11155557 035 $a(DE-He213)978-3-540-44625-5 035 $a(MiAaPQ)EBC3071724 035 $a(PPN)155196944 035 $a(BIP)7336004 035 $a(EXLCZ)991000000000233213 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNon-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners /$fby Thomas Kerler, Volodymyr V. Lyubashenko 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (VI, 383 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1765 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-42416-4 320 $aIncludes bibliographical references and index. 327 $aand Summary of Results -- The Double Category of Framed, Relative 3-Cobordisms -- Tangle-Categories and Presentation of Cobordisms -- Isomorphism between Tangle and Cobordism Double Categories -- Monoidal categories and monoidal 2-categories -- Coends and construction of Hopf algebras -- Construction of TQFT-Double Functors -- Generalization of a modular functor -- From Quantum Field Theory to Axiomatics -- Double Categories and Double Functors -- Thick tangles. 330 $ad + 1-dimensional manifold, whose is a union of d-dimensional boundary disjoint v manifolds and d, a linear : -+ The manifold -Zod V(Md+l) V(Zod) V(Zld). ma- is with the orientation. The axiom in that z0g, Zod opposite gluing [Ati88] requires if we two such d + 1-manifolds a common d-subma- glue together along (closed) fold of in their the linear for the has to be the boundaries, composite compo- map tion of the linear of the individual d + 1-manifolds. maps the of and as in we can state categories functors, [Mac88], Using language axioms as follows: concisely Atiyah's very Definition 0.1.1 A in dimension d is a ([Ati88]). topological quantumfield theory between monoidal functor symmetric categories [Mac881 asfollows: V : --+ k-vect. Cobd+1 finite Here k-vect denotes the whose are dimensional v- category, objects for field tor over a field k, which we assume to be instance, a perfect, spaces The of of characteristic 0. set between two vector is morphisms, simply spaces the set of linear with the usual The has as composition. category Cobd+1 maps manifolds. such closed oriented d-dimensional A between two objects morphism. Zd d oriented d 1-- d-manifolds and is a + 1-cobordism, an + Zod meaning gMd+l = Zd is the d- mensional manifold, Md+l, whose Lj boundary _ZOd of the d-manifolds. consider union two we as joint (Strictly speaking morphisms cobordisms modulo relative Given another or homeomorphisms diffeomorphisms). 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1765 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebra, Homological 606 $aManifolds (Mathematics) 606 $aMathematical physics 606 $aCommutative Rings and Algebras 606 $aCategory Theory, Homological Algebra 606 $aManifolds and Cell Complexes 606 $aTheoretical, Mathematical and Computational Physics 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aAlgebra, Homological. 615 0$aManifolds (Mathematics) 615 0$aMathematical physics. 615 14$aCommutative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 615 24$aManifolds and Cell Complexes. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a510 s 676 $a530.14/3 686 $a81T05$2msc 686 $a57N10$2msc 686 $a18D05$2msc 700 $aKerler$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$053255 702 $aLyubashenko$b Volodymyr V$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144598203321 996 $aNon-semisimple topological quantum field theories for 3-manifolds with corners$9262224 997 $aUNINA