The universal Cannon--Thurston maps and the boundary of the curve complex

Details The universal Cannon--Thurston maps and the boundary of the curve complex The universal Cannon--Thurston maps and the boundary of the curve complex

2008-08-26

arxiv.org/abs/0808.3521v2

Comment. Math. Helv. Volume 86, Issue 4, 2011, pp. 769-816

Mathematics

Geometric Topology

v2. Minor reorganization and revisions throughout. Several typos fixed

Scientific paper

10.4171/CMH/240

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.

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