On the number and location of short geodesics in moduli space
Geometric Topology
2014-02-26 v1 Dynamical Systems
Abstract
A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
Keywords
Cite
@article{arxiv.1110.6434,
title = {On the number and location of short geodesics in moduli space},
author = {Christopher J. Leininger and Dan Margalit},
journal= {arXiv preprint arXiv:1110.6434},
year = {2014}
}
Comments
23 pages, 1 figure