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

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

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English

Springer Verlag, Singapore
26 July 2023

Mathematical foundations; Algebra; Algebraic topology; Mathematical physics

Series: SpringerBriefs in Mathematical Physics

Summary
Details

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.

By: Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 1st ed. 2023
Volume: 44
Dimensions: Height: 235mm, Width: 155mm,
Weight: 142g
ISBN: 9789811946448
ISBN 10: 9811946442
Series: SpringerBriefs in Mathematical Physics
Pages: 68
Publication Date: 26 July 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active