Complete Lorentz spacetimes in dimension three, part 2- Jeffrey Danciger

Conference Title: GEAR Retreat 2012 Theme: Geometric Structures and Teichmuller Spaces (5 of 5) Title: Complete Lorentz spacetimes in dimension three, part 2 Speaker: Jeffrey Danciger, UT Austin; Date and Time: Friday August 10, 15:20 Description: A complete flat Lorentz spacetime in dimension three is a quotient of R3 by a discrete group acting properly by affine O(2, 1) transformations. In the interesting cases, the linear part of the action is the fundamental group of a noncompact hyperbolic surface, which we assume to be convex cocompact, and the translational part of the action corresponds to an infinitesimal deformation of this surface group. Following work of Gueritaud and Kassel in the negatively curved (AdS) case, we prove that such an action is proper if and only if this group-level deformation is realized by a deformation of the surface that everywhere contracts distances at a uniform rate. We then give two applications. 1) Tameness: A complete flat spacetime is diffeomorphic to a handle body. 2) Geometric degeneration: A complete flat spacetime is the limit of collapsing negatively curved (AdS) spacetimes. Joint work with Kassel and Gueritaud. Sponsor: GEAR Network Local host: UIUC Dept of Mathematics Funding provided by: NSF Research Networks in Mathematical SciencesAbstract: Jeffrey Danciger, in this GEAR Retreat 2012 session on Geometric Structures and Teichmuller Spaces, will discuss tameness and geometric degeneration in relation to Lorentz spacetimes and surface deformations.