Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strong equivariant deformation retraction from the homeomorphism group
  of the projective plane to the special orthogonal group   This is the third paper in a series on oriented matroids and Grassmannians.
We construct a $(\mathrm{O}_3\times\mathbb{Z}_2)$-equivariant strong
deformation retraction from the homeomorphism group of the 2-sphere to
$\mathrm{O}_3$, where the action of $\mathbb{Z}_2$ is generated by antipodal
reflection acting on the right, and $\mathrm{O}_3$ acts on the left by
isometry. Quotienting by the antipodal map induces a
$\mathrm{SO}_3$-equivariant strong deformation retraction from the
homeomorphism group of the projective plane to $\mathrm{SO}_3$. The same holds
for subgroups of homeomorphisms that preserve the system of null sets. This
confirms a conjecture of Mary-Elizabeth Hamstrom.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: q-bio