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