LEADER 03233nam 22006135 450 001 9910736002203321 005 20251113182836.0 010 $a981-19-4645-0 024 7 $a10.1007/978-981-19-4645-5 035 $a(MiAaPQ)EBC30666768 035 $a(Au-PeEL)EBL30666768 035 $a(DE-He213)978-981-19-4645-5 035 $a(PPN)272252859 035 $a(CKB)27860984600041 035 $a(EXLCZ)9927860984600041 100 $a20230725d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I /$fby Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (76 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v44 311 08$aPrint version: Lentner, Simon Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I Singapore : Springer,c2023 9789811946448 327 $aMapping class groups -- Tensor categories -- Derived functors. 330 $aThe book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors. It is natural to ask whether this is indeed the case. The book carefully approaches this question by first providing a detailed introduction to surfaces and their mapping class groups. Thereafter, it explains how representations of these groups are constructed in topological field theory, using an approach via nets and ribbon graphs. These tools are then used to show that the mapping class groups indeed act on the so-called derived block spaces. Toward the end, the book explains the relation to Hochschild cohomology of Hopf algebras and the modular group. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v44 606 $aMathematical physics 606 $aAlgebraic topology 606 $aAlgebra, Homological 606 $aMathematical Physics 606 $aAlgebraic Topology 606 $aCategory Theory, Homological Algebra 615 0$aMathematical physics. 615 0$aAlgebraic topology. 615 0$aAlgebra, Homological. 615 14$aMathematical Physics. 615 24$aAlgebraic Topology. 615 24$aCategory Theory, Homological Algebra. 676 $a530.15423 700 $aLentner$b Simon$01380453 701 $aMierach$b Svea Nora$01380454 701 $aSchweigert$b Christoph$061448 701 $aSommerhäuser$b Yorck$067460 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910736002203321 996 $aHochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I$93421890 997 $aUNINA