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

Abstract

To each once-punctured-torus bundle, $T_{\varphi }$, over the circle with pseudo-Anosov monodromy $\varphi$, there are associated two tessellations of the complex plane: one, $\Delta (\varphi )$, is (the projection from $\infty$ of) the triangulation of a horosphere at $\infty$ induced by the canonical decomposition into ideal tetrahedra, and the other, $CW(\varphi )$, 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 $\infty$. In this paper, we study the relation between $\Delta (\varphi )$ and $CW(\varphi )$.

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References in corpus (2)

• On canonical triangulations of once-punctured torus bundles and two-bridge link complements
• Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics

Cited by in corpus (4)

• Veering triangulations and Cannon-Thurston maps
• A variation of McShane's identity for 2-bridge links
• Experimental statistics of veering triangulations
• Cohomology fractals, Cannon-Thurston maps, and the geodesic flow