On hyperbolic once-punctured-torus bundles

James W. Cannon, Warren Dicks

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


For a hyperbolic once-punctured-torus bundle over a circle, a choice of normalization determines a family of arcs in the Riemann sphere. We show that, in each arc in the family, the set of cusps is dense and forms a single orbit of a finitely generated semigroup of Möbius transformations. This was previously known for the case of the complement of the figure-eight knot.
Original languageEnglish
Pages (from-to)141-183
JournalGeometriae Dedicata
Publication statusPublished - 1 Dec 2002


  • Cannon-Thurston map
  • Fractal arc
  • Free group
  • Hyperbolic torus bundle

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