Automorphisms of fine curve graphs for nonorientable surfaces
Geometric Topology
2025-04-02 v2
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 of genus is isomorphic to the homeomorphism group of .
Keywords
Cite
@article{arxiv.2303.16381,
title = {Automorphisms of fine curve graphs for nonorientable surfaces},
author = {Mitsuaki Kimura and Erika Kuno},
journal= {arXiv preprint arXiv:2303.16381},
year = {2025}
}
Comments
14 pages, 1 figure. arXiv admin note: text overlap with arXiv:2108.04872 by other authors