3-manifolds which are spacelike slices of flat spacetimes

Published in Classical and Quantum Gravity, 2001

Recommended citation: Kevin P. Scannell. 3-manifolds which are spacelike slices of flat spacetimes. Classical and Quantum Gravity, 18(9):1691–1701, 2001. https://kevinscannell.com/files/slice.pdf

DOI: doi:10.1088/0264-9381/18/9/306

Abstract: We continue work initiated in a 1990 preprint of Mess giving a geometric parametrization of the moduli space of classical solutions to Einstein’s equations in (2+1) dimensions with cosmological constant Λ = 0 or -1 (the case of Λ = +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 M3 arise as spacelike slices of flat spacetimes, and by finding all possible holonomy homomorphisms π1(M3)→ISO(3,1).