TY  - GEN
N2  - 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.
DO  - 10.1007/978-981-19-4645-5
DO  - doi
AB  - 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.
T1  - Hochschild cohomology, modular tensor categories, and mapping class groups I /
AU  - Lentner, Simon,
AU  - Mierach, Svea Nora,
AU  - Schweigert, Christoph,
AU  - Sommerhäuser, Yorck,
VL  - volume 44
CN  - QC20.7.H65
ID  - 1472076
KW  - Homology theory.
KW  - Tensor algebra.
KW  - Mappings (Mathematics)
SN  - 9789811946455
SN  - 9811946450
TI  - Hochschild cohomology, modular tensor categories, and mapping class groups I /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-4645-5
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-19-4645-5
ER  -