Effective mapping class group dynamics I: Counting lattice points in Teichm\"uller space
Dynamical Systems
2021-04-06 v2 Geometric Topology
Abstract
We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\"uller space that lie within a Teichm\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani.
Cite
@article{arxiv.2010.03123,
title = {Effective mapping class group dynamics I: Counting lattice points in Teichm\"uller space},
author = {Francisco Arana-Herrera},
journal= {arXiv preprint arXiv:2010.03123},
year = {2021}
}
Comments
Updated title, abstract, and introduction. Improved quality of figures. Other minor changes. 51 pages, 5 figures