Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Topological Invariant for Modular Fusion Categories   The modular data of a modular category $\mathcal{C}$, consisting of the
$S$-matrix and the $T$-matrix, is known to be an incomplete invariant of
$\mathcal{C}$. More generally, the invariants of framed links and knots defined
by a modular category as part of a topological quantum field theory can be
viewed as numerical invariants of the category. Among these invariants, we
study the invariant defined by the Borromean link colored by three objects.
Thus we obtain a tensor that we call $B$. We derive a formula for the Borromean
tensor for the twisted Drinfeld doubles of finite groups. Along with $T$, it
distinguishes the $p$ non-equivalent modular categories of the form
$\mathcal{Z}({\rm Vec}_G^\omega)$ for $G$ the non-abelian group
$\mathbb{Z}/q\mathbb{Z} \rtimes \mathbb{Z}/p\mathbb{Z}$, which are not
distinguished by the modular data.

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The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org