Event time:

Thursday, March 24, 2005 - 11:30am to Wednesday, March 23, 2005 - 7:00pm

Location:

431 DL

Speaker:

Feng Luo

Speaker affiliation:

Rutgers and Yale

Event description:

We propose a generalization of Casson and Rivin’s program of finding

hyperbolic structures on compact ideally triangulated 3-manifolds with

torus boundary to all closed triangulated 3-manifolds. In the

generalization, the concepts of angle structure and its volume are

introduced for 3-simplices and triangulated closed 3-manifolds. It is

shown that the critical points of the volume function defined on the

space of all angle structures are closely related to the constant

curvature metrics on 3-manifolds. It is also shown that the volume

function can be extended continuously to the compact closure of the

space of all angle structures.