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Automorphisms of smooth fine curve graphs

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arxiv 2410.21463 v2 pith:RA5JYE2S submitted 2024-10-28 math.GT

Katherine Williams Booth This is my paper · ORCID
classification math.GT
keywords automorphismscurvefinegraphsclosedconsidercontinuouslycurves
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abstract

In this paper, we consider the automorphisms of fine curve graphs restricted to continuously $k$-differentiable curves. We show that for closed surfaces with genus at least 2, they are induced by homeomorphisms of the surface.

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  1. Automorphisms of fine curve graphs of planar surfaces

    math.GT 2025-06 conditional novelty 6.0 of 10

    For a sphere with at least seven punctures, the automorphism group of the fine curve graph is naturally isomorphic to the homeomorphism group of the surface.

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