Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy Coherent Mapping Class Group Actions and Excision for
  Hochschild Complexes of Modular Categories   Given any modular category $\mathcal{C}$ over an algebraically closed field
$k$, we extract a sequence $(M_g)_{g\geq 0}$ of $\mathcal{C}$-bimodules. We
show that the Hochschild chain complex $CH(\mathcal{C};M_g)$ of $\mathcal{C}$
with coefficients in $M_g$ carries a canonical homotopy coherent projective
action of the mapping class group of the surface of genus $g+1$. The ordinary
Hochschild complex of $\mathcal{C}$ corresponds to $CH(\mathcal{C};M_0)$.
  This result is obtained as part of the following more comprehensive
topological structure: We construct a symmetric monoidal functor
$\mathfrak{F}_{\mathcal{C}}:\mathcal{C}\text{-}\mathsf{Surf}^{\mathsf{c}}\to\mathsf{Ch}_k$
with values in chain complexes over $k$ defined on a symmetric monoidal
category of surfaces whose boundary components are labeled with projective
objects in $\mathcal{C}$. The functor $\mathfrak{F}_{\mathcal{C}}$ satisfies an
excision property which is formulated in terms of homotopy coends. In this
sense, any modular category gives naturally rise to a modular functor with
values in chain complexes. In zeroth homology, it recovers Lyubashenko's
mapping class group representations.
  The chain complexes in our construction are explicitly computable by choosing
a marking on the surface, i.e. a cut system and a certain embedded graph. For
our proof, we replace the connected and simply connected groupoid of cut
systems that appears in the Lego-Teichm\"uller game by a contractible Kan
complex.

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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph