English

Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid

Geometric Topology 2014-10-01 v2

Abstract

In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus g=2,3,4,5,8 as well as Lanneau and Thiffeault's conjectural minima for orientable mapping classes, when g = 2,4 (mod 6). Our examples also show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when g = 4,6,8.

Keywords

Cite

@article{arxiv.0909.4517,
  title  = {Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid},
  author = {Eriko Hironaka},
  journal= {arXiv preprint arXiv:0909.4517},
  year   = {2014}
}

Comments

16 pages. 5 figures. Contains minor corrections to previous submission.

R2 v1 2026-06-21T13:50:11.973Z