I’ll discuss a simple observation about a construction of

Thurston’s, from which 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 Teichmuller 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.

# On groups generated by two positive multi-twists: Teichm"uller curves and Lehmer’s number

Event time:

Thursday, November 4, 2004 - 11:30am to Wednesday, November 3, 2004 - 7:00pm

Location:

431 DL

Speaker:

Chris Leininger

Speaker affiliation:

Columbia

Event description: