An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids

Eiko Kin; Mitsuhiko Takasawa

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arXiv · 0711.3009

An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids

Eiko Kin·Mitsuhiko Takasawa

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Abstract

The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids with arbitrarily small dilatation such that the mapping torus obtained from such braid has 2 cusps and has an arbitrarily large volume.

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Eiko Kin, Mitsuhiko Takasawa. 2007-11-19. An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids. https://arxiv.org/abs/0711.3009

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