Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A universal exponent for homeomorphs   We prove a uniform bound on the topological Tur\'an number of an arbitrary
two-dimensional simplicial complex $S$: any $n$-vertex two-dimensional complex
with at least $C_S n^{3-1/5}$ facets contains a homeomorphic copy of $S$, where
$C_S > 0$ is an absolute constant depending on $S$ alone. This result, a
two-dimensional analogue of a classical result of Mader for one-dimensional
complexes, sheds some light on an old problem of Linial from 2006.

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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: eess