The topological and geometrical finiteness of complete flat Lorentzian 3-manifolds with free fundamental groups
Year: 2012
Type: preprint
Abstract: I We prove the topological tameness of a 3-manifold with a free fundamental group admitting a complete flat Lorentzian metric; i.e., a Margulis space-time isomorphic to the quotient of the complete flat Lorentzian space by the free and properly discontinuous isometric action of the free group of rank ≥ 2. I We will use our particular point of view that a Margulis space-time is a real projective manifold in an essential way. I The basic tools are a bordification by a closed RP2-surface with a free holonomy group, the important work of Goldman, Labourie, and Margulis on geodesics in the Margulis space-times and the 3-manifold topology. I Finally, we show that Margulis space-times are geometrically finite under our definition. I The tameness and many other results are also obtained indepedently by Jeff Danciger, Fanny Kassel and Francois Gueritaud.
Source: arXiv (Cornell University)
Author: Suhyoung Choi
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1621418307