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 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.
Original language | English (US) |
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Pages (from-to) | 1301-1359 |
Number of pages | 59 |
Journal | Geometry and Topology |
Volume | 8 |
DOIs | |
State | Published - Oct 19 2004 |
Externally published | Yes |
Keywords
- Coxeter
- Dehn twist
- Lehmer
- Mapping class group
- Pseudo-Anosov
- Teichmüller
ASJC Scopus subject areas
- Geometry and Topology