Homotopy types of fine curve and fine arc complexes
Geometric Topology
2026-02-11 v1
Abstract
The fine curve complex of a surface is a simplicial complex whose vertices are essential simple closed curves and whose -simplices are collections of disjoint curves. We prove that the fine curve complex is homotopy equivalent to the curve complex. We also prove that the fine arc complex is contractible.
Keywords
Cite
@article{arxiv.2602.09897,
title = {Homotopy types of fine curve and fine arc complexes},
author = {Ryan Dickmann and Zachary Himes and Alexander Nolte and Roberta Shapiro},
journal= {arXiv preprint arXiv:2602.09897},
year = {2026}
}
Comments
10 pages, 3 figures