Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering the topology of surfaces from cluster algebras   We present an effective method for recovering the topology of a bordered
oriented surface with marked points from its cluster algebra. The information
is extracted from the maximal triangulations of the surface, those that have
exchange quivers with maximal number of arrows in the mutation class. The
method gives new proofs of the automorphism and isomorphism problems for the
surface cluster algebras, as well as the uniqueness of the
Fomin-Shapiro-Thurston block decompositions of the exchange quivers of the
surface cluster algebras. The previous proofs of these results followed a
different approach based on Gu's direct proof of the last result. The method
also explains the exceptions to these results due to pathological problems with
the maximal triangulations of several surfaces.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg