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• W2618098817 abstract "Let $$mathrm {Mod}(S_g)$$ denote the mapping class group of the closed orientable surface $$S_g$$ of genus $$gge 2$$ . 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 Teichmüller space $$mathrm {Teich}(S_g)$$ . When H is cyclic with $$|H| ge 3$$ , 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 $$ge 3$$ , we derive a computable optimal upper bound for the restriction $$mathrm {sys}: mathrm {Fix}(H) rightarrow mathbb {R}^+$$ 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." @default.
• W2618098817 created "2017-06-05" @default.
• W2618098817 creator A5062010264 @default.
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• W2618098817 date "2022-09-16" @default.
• W2618098817 modified "2023-10-14" @default.
• W2618098817 title "Geometric realizations of cyclic actions on surfaces: II" @default.
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• W2618098817 doi "https://doi.org/10.1007/s10711-022-00729-z" @default.
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