10/7/2004

Greg McShane
Toulouse

Simple geodesics and identities old and new

The set of simple geodesics and its completion the set of geodesic laminations is of fundamental importance in many questions in low dimensional topology and mathematical physics. We shall discuss the so-called McShane identity for Teichmuller space and various generalizations due to Bowditch, Mirzikhani, Sakuma et al. relating them to Diophantine approximation and Mosher's ideas on continued fraction expansions for train tracks. We will touch on semiconjugacies between group actions on the sphere and possible frameworks for generalizing to more general deformation spaces.