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

Christopher J. Leininger, Mahan Mj, Saul Schleimer

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)769-816
Number of pages48
JournalCommentarii Mathematici Helvetici
Volume86
Issue number4
DOIs
StatePublished - 2011

Keywords

  • Cannon-Thurston map
  • Curve complex
  • Ending lamination
  • Mapping class group

ASJC Scopus subject areas

  • Mathematics(all)

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