Automorphisms of some variants of fine graphs

Le Roux, Frédéric; Wolff, Maxime

doi:10.2140/agt.2024.24.4697

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Automorphisms of some variants of fine graphs

Frédéric Le Roux and Maxime Wolff

Algebraic & Geometric Topology 24 (2024) 4697–4730

DOI: 10.2140/agt.2024.24.4697

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 $g \geq 2$ , 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.

Keywords

fine curve graph, homeomorphisms of surfaces

Mathematical Subject Classification

Primary: 37E30, 57K20

References

Publication

Received: 14 November 2022

Revised: 31 March 2023

Accepted: 22 May 2023

Published: 17 December 2024

Authors

Frédéric Le Roux
Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586, CNRS, Univ. Paris Diderot, Sorbonne Paris France

Maxime Wolff
Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586, CNRS, Univ. Paris Diderot, Sorbonne Paris France

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Volume 24, issue 8 (2024)