Ordering curves on surfaces
Geometric Topology
2025-06-10 v1
Abstract
We study the order of lengths of closed geodesics on hyperbolic surfaces. Our first main result is that the order of lengths of curves determine a point in Teichm\"uller space. In an opposite direction, we identify classes of curves whose order never changes, independently of the choice of hyperbolic metric. We use this result to identify short curves with small intersections on pairs of pants.
Keywords
Cite
@article{arxiv.2506.06481,
title = {Ordering curves on surfaces},
author = {Hugo Parlier and Hanh Vo and Binbin Xu},
journal= {arXiv preprint arXiv:2506.06481},
year = {2025}
}
Comments
27 pages, 8 figures