Hyperbolic spaces in Teichm\"uller spaces
Geometric Topology
2013-02-06 v2 Metric Geometry
Abstract
We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H^n almost-isometrically embeds into the Teichm\"uller space of S, with quasi-convex image lying in the thick part. As a consequence, H^n quasi-isometrically embeds in the curve complex of S.
Cite
@article{arxiv.1110.6526,
title = {Hyperbolic spaces in Teichm\"uller spaces},
author = {Christopher J. Leininger and Saul Schleimer},
journal= {arXiv preprint arXiv:1110.6526},
year = {2013}
}
Comments
22 pages, revised to reflect referee's comments