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Automorphisms of fine curve graphs for nonorientable surfaces

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  16 January 2025

Mitsuaki Kimura  and
Erika Kuno
Mitsuaki Kimura
Affiliation:
Department of Mathematics, Osaka Dental University, Hirakata, Osaka, Japan
Erika Kuno*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan
*
Corresponding author: Erika Kuno; Email: [email protected]
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Abstract

The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consisting of essential simple closed curves in the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine curve graph of a closed orientable surface is isomorphic to the homeomorphism group of the surface. In this paper, based on their argument, we prove that the automorphism group of the fine curve graph of a closed nonorientable surface $N$ of genus $g \geq 4$ is isomorphic to the homeomorphism group of $N$.

Keywords

Homeomorphism groupsfine curve graphsnonorientable surfaces

MSC classification

Secondary: 20F65: Geometric group theory 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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References

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