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

Christopher J. Leininger; Mahan Mj; Saul Schleimer

doi:10.4171/cmh/240

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arXiv · 0808.3521

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

Christopher J. Leininger·Mahan Mj·Saul Schleimer

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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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Christopher J. Leininger, Mahan Mj, Saul Schleimer. 2009-02-17. The universal Cannon--Thurston maps and the boundary of the curve complex. https://doi.org/10.4171/cmh%2F240

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