On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane

Warren Dicks, Makoto Sakuma

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

To each once-punctured-torus bundle, Tφ, over the circle with pseudo-Anosov monodromy φ, there are associated two tessellations of the complex plane: one, Δ(φ), is (the projection from ∞ of) the triangulation of a horosphere at ∞ induced by the canonical decomposition into ideal tetrahedra, and the other, CW(φ), is a fractal tessellation given by the Cannon-Thurston map of the fiber group switching back and forth between gray and white each time it passes through ∞. In this paper, we fully describe the relation between Δ(φ) and CW(φ). © 2010 Elsevier B.V.
Original languageEnglish
Pages (from-to)1873-1899
JournalTopology and its Applications
Volume157
Issue number12
DOIs
Publication statusPublished - 1 Aug 2010

Keywords

  • Fractal tessellation
  • Hyperbolic once-punctured-torus bundles
  • Jørgensen triangulation

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