The universal Cannon–Thurston map and the boundary of the curve complex
Leininger, Christopher, Mj, Mahan and Schleimer, Saul. (2011) The universal Cannon–Thurston map and the boundary of the curve complex. Commentarii Mathematici Helvetici, Vol.86 (No.4). pp. 769-816. ISSN 0010-2571Full text not available from this repository.
Official URL: http://dx.doi.org/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.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Commentarii Mathematici Helvetici|
|Publisher:||European Mathematical Society Publishing House|
|Page Range:||pp. 769-816|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||NSF , UGC|
|Grant number:||DMS-0603881 DMS-0508971 (NSF)|
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