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

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

Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser

Springer
Collection: SpringerBriefs in Mathematical Physics
Publication date : 2023-07-25

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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.

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About the book

Author

Simon Lentner , Svea Nora Mierach , Christoph Schweigert , Yorck Sommerhäuser

Imprint

Springer

Collection

SpringerBriefs in Mathematical Physics

Publication date

2023-07-25

Pages

68 pages

Print ISBN

9789811946448

Language

English

Ebook informations

EAN PDF

9789811946455

Price

£44.99

Copy count 0

Print count 6

File size 768 Ko

Informations accessibility

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About author(s)

Simon Lentner

Svea Nora Mierach

Christoph Schweigert

Yorck Sommerhäuser

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