English

Automorphisms of fine curve graphs of planar surfaces

Geometric Topology 2025-06-09 v1

Abstract

The fine curve graph of a surface is the graph whose vertices are simple closed essential curves in the surface and whose edges connect disjoint curves. In this paper, we prove that the automorphism group of the fine curve graph of a surface is naturally isomorphic to the homeomorphism group of the surface for boundaryless planar surfaces with at least 7 punctures.

Keywords

Cite

@article{arxiv.2506.06142,
  title  = {Automorphisms of fine curve graphs of planar surfaces},
  author = {Roberta Shapiro and Rohan Wadhwa and Arthur Wang and Yuchong Zhang},
  journal= {arXiv preprint arXiv:2506.06142},
  year   = {2025}
}

Comments

11 pages, 4 figures