Flat Lorentz 3-Manifolds and Cocompact Fuchsian Groups

Details Flat Lorentz 3-Manifolds and Cocompact Fuchsian Groups Flat Lorentz 3-Manifolds and Cocompact Fuchsian Groups

2000-05-31

arxiv.org/abs/math/0005292v1

Crystallographic groups and their generalizations (Kortrijk, 1999), 135--145, Contemp. Math., 262, Amer. Math. Soc., Providenc

Mathematics

Differential Geometry

to appear in "Crystallographic Groups and their Generalizations II," Contemporary Mathematics

Scientific paper

This paper gives a new proof of a result of Geoff Mess that the linear
holonomy group of a complete flat Lorentz 3-manifold cannot be cocompact in
SO(2,1). The proof uses a signed marked Lorentzian length-spectrum invariant
developed by G.Margulis, reinterpreted in terms of deformations of hyperbolic
surfaces.

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