Simple curves on surfaces
Geometric Topology
2007-05-23 v2 Differential Geometry
Group Theory
Abstract
We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L^{6g+2b+2c-6}. This has been conjectured for some time.
Cite
@article{arxiv.math/9907041,
title = {Simple curves on surfaces},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/9907041},
year = {2007}
}
Comments
16 pages, many figures