The universal Cannon--Thurston maps and the boundary of the curve complex
Geometric Topology
2011-10-31 v2 Group Theory
Abstract
In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal Cannon--Thurston map from a subset of the circle at infinity for the closed surface group onto the boundary of the curve complex of the once-punctured surface. Using the techniques we have developed, we also show that the boundary of this curve complex is locally path-connected.
Cite
@article{arxiv.0808.3521,
title = {The universal Cannon--Thurston maps and the boundary of the curve complex},
author = {Christopher J. Leininger and Mahan Mj and Saul Schleimer},
journal= {arXiv preprint arXiv:0808.3521},
year = {2011}
}
Comments
v2. Minor reorganization and revisions throughout. Several typos fixed