Year: 2026
Type: preprint
Abstract: By a celebrated result of Birman and Series, the set of simple complete geodesics form a nowhere dense subset of a hyperbolic surface. We show that a segment of finite length is in a (small) neighborhood of this set if it can be "extended simply" in both directions for long enough. We deduce that, for large enough genus $g$, there exist surfaces with a Birman-Series set that is roughly $\frac{1}{g^{\sfrac{2}{3}}}$-dense.
Source: arXiv (Cornell University)
Authors: Buser, Peter, Parlier, Hugo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221525445