On cusps of hyperbolic once-punctured torus bundles over the circle

Author:

López-López Jorge L.,Villicaña-Molina Yesenia

Abstract

The geometry of certain canonical triangulation of once-punctured torus bundles over the circle is applied to the problem of computing their cusp tori. We are also concerned with the problem of finding the limit points of the set formed by such cusp tori, inside the moduli space of the torus. Our discussion generalizes examples which were elaborated by H. Helling (unpublished) and F. Guéritaud.

Publisher

Universidad Nacional de Colombia

Subject

General Mathematics

Reference15 articles.

1. H. Akiyoshi, On the Ford domains of once-punctured torus groups, Hyperbolic spaces and related topics, RIMS, Kyoto, vol. 1104, 1999, pp. 109-121.

2. W. Dicks and D. J. Wright, On hyperbolic once-punctured-torus bundles IV: Automata for lightning curves, Topology Appl. 159 (2012), 98-132.

3. D. Epstein and C. Petronio, An exposition of Poincaré's polyhedron theorem, Enseign. Math. 40 (1994), 113-170.

4. F. Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006), no. 3, 1239-1284.

5. H. Helling, The trace field of a series of hyperbolic manifolds, Preprint 99-072, SBF 343, Bielefeld, 1999.

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