Speaker: 

Professor Jianguo Cao

Institution: 

Notre Dame

Time: 

Tuesday, November 4, 2008 - 4:00pm

Location: 

RH 306

In this lecture, we present a new proof of Perelman's collapsing theorem for 3-manifolds with boundary which is needed for his work on Thurston's Geometrization Conjecture. Among other things, we use an observation of Hamilton-Perelman on incompressible tori boundary for Ricci flow with surgery on thick part of a 3-manifold. Starting from incompressible tori boundary of thin part of 3-manifold, we found that there is an injective F-structure in the sense of Cheeger-Gromov. Consequently, the part of a 3-manifold for Ricci flow with surgery becomes an aspherical graph-manifold, Perelman's collapsing theorem for 3-manifolds follows.