Universal Cannon-Thurston maps and the boundary of the curve complex

Leininger, Christopher J. ; Mahan, Mj. ; Saul, Schleimerz (2011) Universal Cannon-Thurston maps and the boundary of the curve complex Commentarii Mathematici Helevetici, 86 (4). pp. 769-816.

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Abstract

The fundamental group of a closed surface of genus at least two admits a natural action 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. Further, we show that the boundary of this curve complex is locally path-connected.

Item Type:Article
Source:Copyright of this article belongs to Swiss Mathematical Society.
ID Code:89537
Deposited On:28 Apr 2012 12:57
Last Modified:19 May 2016 04:04

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