Hochschild cohomology, modular tensor categories, and mapping class groups I / Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser.
Lentner, Simon, author.; Mierach, Svea Nora, author.; Schweigert, Christoph, author.; Sommerhäuser, Yorck, 1966- author.
2023
QC20.7.H65
Available Online

Linked e-resources

Linked Resource
Online Access
Concurrent users
Unlimited
Authorized users
Authorized users
Document Delivery Supplied
Can lend chapters, not whole ebooks

Details

Title
Hochschild cohomology, modular tensor categories, and mapping class groups I / Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser.
Author
Lentner, Simon, author.
ISBN
9789811946455 (electronic bk.)
9811946450 (electronic bk.)
9789811946448
9811946442
DOI
https://doi.org/10.1007/978-981-19-4645-5
Published
Singapore : Springer, [2023]
Copyright
©2023
Language
English
Description
1 online resource (ix, 68 pages) : illustrations (chiefly color).
Item Number
10.1007/978-981-19-4645-5 doi
Call Number
QC20.7.H65
Dewey Decimal Classification
530.15423
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 1, 2023).
Added Author
Mierach, Svea Nora, author.
Schweigert, Christoph, author.
Sommerhäuser, Yorck, 1966- author.
Series
SpringerBriefs in mathematical physics ; v. 44.
Available in Other Form
Print version: 9789811946448
Linked Resources
Online Access
Record Appears in
Online Resources > Ebooks
All Resources
Intro
Contents
Introduction
Chapter 1 Mapping Class Groups
1.1 The classification of surfaces
1.2 The fundamental group
1.3 Mapping class groups
1.4 Dehn twists
1.5 Braidings
1.6 The action on the fundamental group
1.7 Dehn twists for special curves
1.8 Dehn twists related to two boundary components
1.9 The capping homomorphism
1.10 The Birman sequence
1.11 Singular homology
1.12 The mapping class group of the torus
1.13 The mapping class group of the sphere
Chapter 2 Tensor Categories
2.1 Finiteness
2.2 Factorizable Hopf algebras

2.3 Coends
2.4 Coends from Hopf algebras
2.5 The block spaces
2.6 Mapping class group representations
2.7 Modular functors
2.8 The case of the torus
Chapter 3 Derived Functors
3.1 Projective resolutions
3.2 Derived block spaces
3.3 The case of the sphere
3.4 Hochschild cohomology
References

Browse Subjects

Show more subjects...

Statistics

from
to
Export