Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Tutte polynomial and toric Nakajima quiver varieties   For a quiver $Q$, we take $\mathcal{M}$ an associated toric Nakajima quiver
variety and $\Gamma$ the underlying graph. In this article, we give a direct
relation between a specialisation of the Tutte polynomial of $\Gamma$, the Kac
polynomial of $Q$ and the Poincar\'e polynomial of $\mathcal{M}$. We do this by
giving a cell decomposition of $\mathcal{M}$ indexed by spanning trees of
$\Gamma$ and `geometrising' the deletion and contraction operators on graphs.
These relations have been previously established by Sturmfels-Hausel and
(Crawley-Boovey)-Van den Bergh, however the methods here are more hands-on.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci