Abstract
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.
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Cannon, J.W., Dicks, W. On Hyperbolic Once-Punctured-Torus Bundles. Geometriae Dedicata 94, 141–183 (2002). https://doi.org/10.1023/A:1020956906487
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DOI: https://doi.org/10.1023/A:1020956906487