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

1. Auflage 2023
ISBN: 978-981-19-4644-8
Verlag: Springer

Buch, Englisch, Band 44, 68 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 137 g

Reihe: SpringerBriefs in Mathematical Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lentner, Simon

Mierach, Svea Nora

Schweigert, Christoph

Sommerhäuser, Yorck

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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