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

• Kin Eiko

  Department of Mathematical and Computing Sciences Tokyo Institute of Technology

• Takasawa Mitsuhiko

  Department of Mathematical and Computing Sciences Tokyo Institute of Technology

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.

Journal

• Kodai Mathematical Journal

  Kodai Mathematical Journal 31 (1), 92-112, 2008

  Department of Mathematics, Tokyo Institute of Technology

Keywords

• mapping class group
• braid
• pseudo-Anosov
• dilatation

Details

• CRID: 1390001205273496832
• NII Article ID: 130004687884
• DOI: 10.2996/kmj/1206454554
• ISSN: 18815472
• ISSN: 03865991
• MRID: 2414236
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed