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Automorphisms of the fine 1-curve graph

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arxiv 2309.16041 v1 pith:HXQEFLYX submitted 2023-09-27 math.GT

Katherine Williams Booth , Daniel Minahan , Roberta Shapiro This is my paper · ORCID
classification math.GT
keywords graphcurvefinesurfaceclosedgroupverticeswhose
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The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is naturally isomorphic to the homeomorphism group of a closed, orientable surface with genus at least one.

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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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