English

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 NN of genus g4g \geq 4 is isomorphic to the homeomorphism group of NN.

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