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

Kin, Eiko; Takasawa, Mitsuhiko

Kodai Math. J., Tome 31 (2008) no. 1, p. 92-112 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-03-15
Classification:

@article{1206454554,
     author = {Kin, Eiko and Takasawa, Mitsuhiko},
     title = {An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids},
     journal = {Kodai Math. J.},
     volume = {31},
     number = {1},
     year = {2008},
     pages = { 92-112},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1206454554}
}

Kin, Eiko; Takasawa, Mitsuhiko. An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids. Kodai Math. J., Tome 31 (2008) no. 1, pp.  92-112. http://gdmltest.u-ga.fr/item/1206454554/