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

Authors
  • Leininger, Christopher J.
  • Mj, Mahan
  • Schleimer, Saul
Type
Published Article
Publication Date
Feb 17, 2009
Submission Date
Aug 26, 2008
Identifiers
DOI: 10.4171/CMH/240
Source
arXiv
License
Yellow
External links

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.

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