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• W3138804178 abstract "Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannian metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for infinite-genus 2-manifolds with no planar ends. Surprisingly, we show there is an uncountable class of such 2-manifolds where every countable group can be realized as an isometry group (namely, those with self-similar end spaces). We apply this result to obtain obstructions to standard group theoretic properties for the groups of homeomorphisms, diffeomorphisms, and the mapping class groups of such 2-manifolds. For example, none of these groups satisfy the Tits Alternative; are coherent; are linear; are cyclically or linearly orderable; or are residually finite. As a second application, we give an algebraic rigidity result for mapping class groups." @default.
• W3138804178 created "2021-03-29" @default.
• W3138804178 creator A5047912173 @default.
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• W3138804178 date "2021-03-23" @default.
• W3138804178 modified "2023-10-13" @default.
• W3138804178 title "Isometry groups of infinite-genus hyperbolic surfaces" @default.
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• W3138804178 doi "https://doi.org/10.1007/s00208-021-02164-z" @default.
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