Curve complexes are rigid
Geometric Topology
2019-12-19 v2
Abstract
Any quasi-isometry of the complex of curves is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.
Cite
@article{arxiv.0710.3794,
title = {Curve complexes are rigid},
author = {Kasra Rafi and Saul Schleimer},
journal= {arXiv preprint arXiv:0710.3794},
year = {2019}
}
Comments
20 pages, two figures, revised to reflect referee comments