On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane |
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Authors: | Warren Dicks Makoto Sakuma |
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Institution: | a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain b Department of Mathematics, Graduate School of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima, Hiroshima 739-8526, Japan |
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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). |
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Keywords: | Hyperbolic once-punctured-torus bundles Fractal tessellation Jø rgensen triangulation |
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