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Hochschild cohomology, modular tensor categories, and mapping class groups I

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hochschild cohomology, modular tensor categories, and mapping class groups Iby Simon Lentner ... [et al.].
other author:	Lentner, Simon.
Published:	Singapore :Springer Nature Singapore :2023.
Description:	ix, 68 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Homology theory.
Online resource:	https://doi.org/10.1007/978-981-19-4645-5
ISBN:	9789811946455$q(electronic bk.)

Hochschild cohomology, modular tensor categories, and mapping class groups I
Hochschild cohomology, modular tensor categories, and mapping class groups I[electronic resource] /by Simon Lentner ... [et al.]. - Singapore :Springer Nature Singapore :2023. - ix, 68 p. :ill. (chiefly color), digital ;24 cm. - SpringerBriefs in mathematical physics,v. 442197-1765 ;. - SpringerBriefs in mathematical physics ;v.1..

Mapping class groups -- Tensor categories -- Derived functors.

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.

ISBN: 9789811946455$q(electronic bk.)

Standard No.: 10.1007/978-981-19-4645-5doiSubjects--Topical Terms:

205880
Homology theory.

LC Class. No.: QC20.7.H65

Dewey Class. No.: 530.15423

Hochschild cohomology, modular tensor categories, and mapping class groups I
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245 0 0 $a Hochschild cohomology, modular tensor categories, and mapping class groups I $h [electronic resource] / $c by Simon Lentner ... [et al.].
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2023.
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490 1 $a SpringerBriefs in mathematical physics, $x 2197-1765 ; $v v. 44
505 0 $a Mapping class groups -- Tensor categories -- Derived functors.
520 $a 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.
650 0 $a Homology theory. $3 205880
650 0 $a Tensor algebra. $3 348467
650 0 $a Mappings (Mathematics) $3 338109
650 1 4 $a Mathematical Physics. $3 522725
650 2 4 $a Algebraic Topology. $3 273784
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Lentner, Simon. $3 958674
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830 0 $a SpringerBriefs in mathematical physics ; $v v.1. $3 683312
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950 $a Mathematics and Statistics (SpringerNature-11649)