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Automorphisms of some variants of fine graphs

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arxiv 2210.05460 v1 pith:LRGY4C66 submitted 2022-10-11 math.GT

Frédéric Le Roux , Maxime Wolff This is my paper · ORCID
classification math.GT
keywords finegraphsurfacescasecurvegraphsgrouphomeomorphism
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abstract

Recently Bowden, Hensel and Webb defined the fine curve graph for surfaces, extending the notion of curve graphs for the study of homeomorphism or diffeomorphism groups of surfaces. Later Long, Margalit, Pham, Verberne and Yao proved that for a closed surface of genus $g\geqslant 2$, the automorphism group of the fine graph is naturally isomorphic to the homeomorphism group of the surface. We extend this result to the torus case $g=1$; in fact our method works for more general surfaces, compact or not, orientable or not. We also discuss the case of a smooth version of the fine graph.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hyperbolicity, topology, and combinatorics of fine curve graphs and variants

    math.GT 2025-01 conditional novelty 7.0 of 10

    The fine k-curve graph is hyperbolic; the finitary curve graph has diameter 2, a contractible flag complex, all countable graphs as induced subgraphs, and automorphism group equal to the homeomorphism group of the surface.

  2. 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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