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

نویسندگان

  • Eiko Kin
  • Mitsuhiko Takasawa
چکیده

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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تاریخ انتشار 2008