03522nam 22006975 450 991073600220332120240522105634.0981-19-4645-010.1007/978-981-19-4645-5(MiAaPQ)EBC30666768(Au-PeEL)EBL30666768(DE-He213)978-981-19-4645-5(PPN)272252859(CKB)27860984600041(EXLCZ)992786098460004120230725d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I /by Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser1st ed. 2023.Singapore :Springer Nature Singapore :Imprint: Springer,2023.1 online resource (76 pages)SpringerBriefs in Mathematical Physics,2197-1765 ;44Print version: Lentner, Simon Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I Singapore : Springer,c2023 9789811946448 Mapping class groups -- Tensor categories -- Derived functors.The 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.SpringerBriefs in Mathematical Physics,2197-1765 ;44Mathematical physicsAlgebraic topologyAlgebra, HomologicalMathematical PhysicsAlgebraic TopologyCategory Theory, Homological AlgebraÀlgebra homològicathubÀlgebra tensorialthubAplicacions (Matemàtica)thubLlibres electrònicsthubMathematical physics.Algebraic topology.Algebra, Homological.Mathematical Physics.Algebraic Topology.Category Theory, Homological Algebra.Àlgebra homològicaÀlgebra tensorialAplicacions (Matemàtica)530.15423Lentner Simon1380453Mierach Svea Nora1380454Schweigert Christoph61448Sommerhäuser Yorck67460MiAaPQMiAaPQMiAaPQBOOK9910736002203321Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I3421890UNINA