On groups generated by two positive multi-twists: Teichmueller curves and Lehmer’s number

Leininger, Christopher J¹

¹ Department of Mathematics, Columbia University, 2990 Broadway MC 4448, New York, New York 10027, USA

Geometry & topology, Tome 8 (2004) no. 3, pp. 1301-1359.

Résumé

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 Teichmüller 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.

Détail

DOI : 10.2140/gt.2004.8.1301

Keywords: Coxeter, Dehn twist, Lehmer, pseudo-Anosov, mapping class group, Teichmüller

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