Solving Thurstons equation on triangulated 3-manifolds
主 题: Solving Thurstons equation on triangulated 3-manifolds
报告人: Prof. LUO Feng (Rutgers University,USA)
时 间: 2010-07-19 16:30 - 17:30
地 点: 北京大学资源大厦1328教室
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.