arXiv subjects

Svea Nora Mierach

Publications and source records attributed to Svea Nora Mierach.

3 recordsLinked to original sources

arXiv2026

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

In the first part of this work, we have, for a not necessarily semisimple modular category, generalized the action of the mapping class groups of surfaces on the spaces of conformal blocks to the so-called derived block spaces. In the second part presented here, we compute this action explicitly in the case of Drinfel'd doubles of finite groups over fields of positive characteristic. To do that, we connect Lyubashenko's approach to mapping class group representations with the theory of representation varieties. In this way, we are able to show that the mapping class group representations on the derived block spaces are in general different from those on the ordinary block spaces.

math.QA↗

arXiv2021

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups

Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action coincides with the known projective action of the mapping class group on the space of chiral conformal blocks. In the case that the surface is a torus and the category is the representation category of a factorizable ribbon Hopf algebra, we recover our previous result on the projective action of the modular group on the Hochschild cohomology groups of the Hopf algebra.

math.QA↗

arXiv2017

Hochschild Cohomology and the Modular Group

It has been shown in previous work that the modular group acts projectively on the center of a factorizable ribbon Hopf algebra. The center is the zeroth Hochschild cohomology group. In this article, we extend this projective action of the modular group to an arbitrary Hochschild cohomology group of a factorizable ribbon Hopf algebra, in fact up to homotopy even to a projective action on the entire Hochschild cochain complex.

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