Einband gross Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

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Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

von

Lentner, SimonMierach, Svea NoraSchweigert, Christoph

BuchKartoniert, Paperback

68 Seiten

Englisch

Springererschienen am26.07.20231st ed. 2023

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.mehr

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KlappentextThe 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.

Zusammenfassung
Discusses conformal field theory in a non-semisimple setting

Uses Lyubashenko s approach via nets and ribbon graphs

Describes the relation to Hochschild cohomology of Hopf algebras

Details

ISBN/GTIN978-981-19-4644-8

ProduktartBuch

EinbandartKartoniert, Paperback

Verlag

Springer

Erscheinungsjahr2023

Erscheinungsdatum26.07.2023

Auflage1st ed. 2023

ReiheSpringerBriefs in Mathematical Physics

Seiten68 Seiten

SpracheEnglisch