Angle structures on tetrahedra and triangulated 3-manifolds

Geometry & Topology
Event time: 
Thursday, March 24, 2005 - 11:30am to Wednesday, March 23, 2005 - 7:00pm
431 DL
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.