Weil-Petersson geometry of Teichmüller spaces and the Thurston classification of surface diffeomorphisms

Sumio Yamada (Cornell)

In this talk I will discuss the geometry of Teichmüller spaces with respect to a Riemannian metric, called the Weil-Petersson metric.  Compared to the better-studied Teichmüller (Finsler) metric, the Weil-Petersson metric suffers from the defect of being incomplete.  It will be demonstrated that by taking the completion of the space, one obtains a more comprehensive picture of the Teichmüller space. In particular  the isometric action of the mapping class group extends to the completion, providing a reformulation of Thurston's classification of surface diffeomorphisms.

Spring 2001 meeting of the PNGS