3-manifolds which are spacelike slices of flat spacetimes

Details 3-manifolds which are spacelike slices of flat spacetimes 3-manifolds which are spacelike slices of flat spacetimes

2000-11-02

arxiv.org/abs/math/0011021v1

Mathematics

Differential Geometry

10 pages

Scientific paper

10.1088/0264-9381/18/9/306

We continue work initiated in a 1990 preprint of Mess giving a geometric parameterization of the moduli space of classical solutions to Einstein's equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has been worked out in the interim by the present author). In this paper we make a first step toward the 3+1-dimensional case by determining exactly which closed 3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).

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