Geometry & Topology, Vol. 8 (2004)
Paper no. 36, pages 1301--1359.
On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
Christopher J Leininger
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.
Coxeter, Dehn twist, Lehmer, pseudo-Anosov, mapping class group, Teichmueller
AMS subject classification.
Primary: 57M07, 57M15.
Secondary: 20H10, 57M25.
DOI: 10.2140/gt.2004.8.1301
E-print: arXiv:math.GT/0304163
Submitted to GT on 16 February 2004.
(Revised 17 August 2004.)
Paper accepted 11 October 2004.
Paper published 19 October 2004.
Notes on file formats
Christopher J Leininger
Department of Mathematics, Columbia University
2990 Broadway MC 4448, New York, NY 10027, USA
Email: clein@math.columbia.edu
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