Immersions of Pants into a Fixed Hyperbolic Surface
Geometric Topology
2007-05-23 v2 Dynamical Systems
Abstract
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T_1(S) x T_1(S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two uniformly random closed geodesics gamma_1, gamma_2 of length within epsilon of L have a high probability of partially bounding an immersed 4-holed sphere whose other boundary components also have length within epsilon of L. Version 2: The coefficient in corollary 1.6 corrected from 16 to 8.
Cite
@article{arxiv.math/0505480,
title = {Immersions of Pants into a Fixed Hyperbolic Surface},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:math/0505480},
year = {2007}
}
Comments
43 pages