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The universal Cannon–Thurston map and the boundary of the curve complex
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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. doi:10.4171/CMH/240 ISSN 0010-2571.
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Official URL: http://dx.doi.org/10.4171/CMH/240
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Commentarii Mathematici Helvetici | ||||
| Publisher: | European Mathematical Society Publishing House | ||||
| ISSN: | 0010-2571 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.86 | ||||
| Number: | No.4 | ||||
| Page Range: | pp. 769-816 | ||||
| DOI: | 10.4171/CMH/240 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | NSF , UGC | ||||
| Grant number: | DMS-0603881 DMS-0508971 (NSF) |
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