Automorphisms of fine curve graphs for nonorientable surfaces

Mitsuaki Kimura; Erika Kuno

doi:10.1017/s001708952400034x

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arXiv · 2303.16381

Automorphisms of fine curve graphs for nonorientable surfaces

Mitsuaki Kimura·Erika Kuno

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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 on 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 $N$.

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BibTeX RIS

Mitsuaki Kimura, Erika Kuno. 2023-03-29. Automorphisms of fine curve graphs for nonorientable surfaces. https://doi.org/10.1017/s001708952400034x

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