Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I (SpringerBriefs in Mathematical Physics, 44)

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

ISBN 10: 9811946442 / ISBN 13: 9789811946448

Published by Springer, 2023

About this Item

Seller Inventory # I-9789811946448

Bibliographic Details

• Title: Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I (SpringerBriefs in Mathematical Physics, 44)
• Publisher: Springer
• Publication Date: 2023
• Language: English
• ISBN 10: 9811946442
• ISBN 13: 9789811946448
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.