Title: Solving Thurston's equation on triangulated 3-manifolds

Speaker： Prof. Feng Luo（Rutgers University, USA）

Time: 4:30-530pm, July 19, 2010

Venue: Room 1328 at BICMR (北京大学资源大厦1328教室）

Abstract: In 1978, Thurston introduced an algebraic equation defined over each triangulated 3-manifold to find hyperbolic structures. Thurston's theory can be considered as a discrete SL(2,C) Chern-Simons theory on the manifold. We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's equation and Haken's normal surface equation. The action functional is the volume. This is a generalization of an earlier program by Casson and Rivin for compact 3-manifolds with torus boundary. Combining the work of Futer-Gueritaud, Segerman-Tillmann and Luo-Tillmann, we obtain a new finite dimensional variational formulation of the Poncare conjecture. This provides a step toward a new proof the Poincare conjecture without using the Ricci flow.