Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric realizations of cyclic actions on surfaces -- II   Let $\mathrm{Mod}(S_g)$ denote the mapping class group of the closed
orientable surface $S_g$ of genus $g\geq 2$. Given a finite subgroup $H$ of
$\mathrm{Mod}(S_g)$, let $\mathrm{Fix}(H)$ denote the set of fixed points
induced by the action of $H$ on the Teichm\"{u}ller space
$\mathrm{Teich}(S_g)$. When $H$ is cyclic with $|H| \geq 3$, we show that
$\mathrm{Fix}(H)$ admits a decomposition as a product of two-dimensional strips
at least one of which is of bounded width. For an arbitrary $H$ with at least
one generator of order $\geq 3$, we derive a computable optimal upper bound for
the restriction $\mathrm{sys} : \mathrm{Fix}(H) \to \mathbb{R}^+$ of the
systole function. Furthermore, we show that in such a case, $\mathrm{Fix}(H)$
is not symplectomorphic to the Euclidean space of the same dimension. Finally,
we apply our theory to recover three well-known results, namely: (a) Harvey's
result giving the dimension of $\mathrm{Fix}(H)$, (b) Gilman's result that $H$
is irreducible if and only if the corresponding orbifold is a sphere with three
cone points, and (c) the Nielsen realization theorem for cyclic groups.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: stat