Ending Laminations and Cannon-Thurston Maps
Geometric Topology
2014-03-18 v4
Abstract
In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian surface groups. In this paper we prove that pre-images of points are precisely end-points of leaves of the ending lamination whenever the Cannon-Thurston map is not one-to-one. In particular, the Cannon-Thurston map is finite-to-one. This completes the proof of the conjectural picture of Cannon-Thurston maps for surface groups.
Cite
@article{arxiv.math/0701725,
title = {Ending Laminations and Cannon-Thurston Maps},
author = {Mahan Mj},
journal= {arXiv preprint arXiv:math/0701725},
year = {2014}
}
Comments
v4: Final version 22pgs 2figures. Includes the main theorem of the appendix arXiv:1002.2090 by Shubhabrata Das and Mahan Mj. To appear in Geometric and Functional Analysis