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001472076 001__ 1472076
001472076 003__ OCoLC
001472076 005__ 20230908003329.0
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001472076 008__ 230730s2023\\\\si\a\\\\ob\\\\000\0\eng\d
001472076 019__ $$a1391437620
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001472076 0247_ $$a10.1007/978-981-19-4645-5$$2doi
001472076 035__ $$aSP(OCoLC)1391327795
001472076 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCQ
001472076 049__ $$aISEA
001472076 050_4 $$aQC20.7.H65
001472076 08204 $$a530.15423$$223/eng/20230801
001472076 1001_ $$aLentner, Simon,$$eauthor.
001472076 24510 $$aHochschild cohomology, modular tensor categories, and mapping class groups I /$$cSimon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser.
001472076 264_1 $$aSingapore :$$bSpringer,$$c[2023]
001472076 264_4 $$c©2023
001472076 300__ $$a1 online resource (ix, 68 pages) :$$billustrations (chiefly color).
001472076 336__ $$atext$$btxt$$2rdacontent
001472076 337__ $$acomputer$$bc$$2rdamedia
001472076 338__ $$aonline resource$$bcr$$2rdacarrier
001472076 4901_ $$aSpringerBriefs in mathematical physics ;$$vvolume 44
001472076 504__ $$aIncludes bibliographical references.
001472076 5050_ $$aIntro -- Contents -- Introduction -- Chapter 1 Mapping Class Groups -- 1.1 The classification of surfaces -- 1.2 The fundamental group -- 1.3 Mapping class groups -- 1.4 Dehn twists -- 1.5 Braidings -- 1.6 The action on the fundamental group -- 1.7 Dehn twists for special curves -- 1.8 Dehn twists related to two boundary components -- 1.9 The capping homomorphism -- 1.10 The Birman sequence -- 1.11 Singular homology -- 1.12 The mapping class group of the torus -- 1.13 The mapping class group of the sphere -- Chapter 2 Tensor Categories -- 2.1 Finiteness -- 2.2 Factorizable Hopf algebras
001472076 5058_ $$a2.3 Coends -- 2.4 Coends from Hopf algebras -- 2.5 The block spaces -- 2.6 Mapping class group representations -- 2.7 Modular functors -- 2.8 The case of the torus -- Chapter 3 Derived Functors -- 3.1 Projective resolutions -- 3.2 Derived block spaces -- 3.3 The case of the sphere -- 3.4 Hochschild cohomology -- References
001472076 506__ $$aAccess limited to authorized users.
001472076 520__ $$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.
001472076 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed August 1, 2023).
001472076 650_0 $$aHomology theory.
001472076 650_0 $$aTensor algebra.
001472076 650_0 $$aMappings (Mathematics)
001472076 655_0 $$aElectronic books.
001472076 7001_ $$aMierach, Svea Nora,$$eauthor.
001472076 7001_ $$aSchweigert, Christoph,$$eauthor.$$1https://isni.org/isni/0000000032797393
001472076 7001_ $$aSommerhäuser, Yorck,$$d1966-$$eauthor.$$1https://isni.org/isni/0000000114415010
001472076 77608 $$iPrint version: $$z9811946442$$z9789811946448$$w(OCoLC)1330196277
001472076 830_0 $$aSpringerBriefs in mathematical physics ;$$vv. 44.
001472076 852__ $$bebk
001472076 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-4645-5$$zOnline Access$$91397441.1
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001472076 980__ $$aBIB
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