On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
Abstract
From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we identify all configurations of curves for which the corresponding groups fail to be free, and show that a subset of these determine the same set of Teichmueller curves as the non-obtuse lattice triangles which were classified by Kenyon, Smillie, and Puchta. We also identify a pseudo-Anosov automorphism whose dilatation is Lehmer's number, and show that this is minimal for the groups under consideration. In addition, we describe a connection to work of McMullen on Coxeter groups and related work of Hironaka on a construction of an interesting class of fibered links.
Keywords
Cite
@article{arxiv.math/0304163,
title = {On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number},
author = {Christopher J. Leininger},
journal= {arXiv preprint arXiv:math/0304163},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper36.abs.html