Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric products of surfaces and the cycle index   We express the signature ${\rm Sign}(SP^m_G(M))$ of the symmetric product
$SP^n(M)$ of an (open) surface $M$ in terms of the cycle index $Z(G;\bar x)$ of
$G$, a polynomial which originally appeared in P{\' o}lya enumeration theory of
graphs, trees, chemical structures etc. The computations are used to show that
there exist punctured Riemann surfaces $M_{g,k}, M_{g',k'}$ such that the
manifolds $SP^{m}(M_{g,k})$ and $SP^{m}(M_{g',k'})$ are often not homeomorphic,
although they always have the same homotopy type provided $2g+k = 2g'+k'$ and
$k,k'\geq 1$.

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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas