Witten's 2+1 gravity on R x (Klein bottle)

Details Witten's 2+1 gravity on R x (Klein bottle) Witten's 2+1 gravity on R x (Klein bottle)

1995-05-17

arxiv.org/abs/gr-qc/9505026v1

Class.Quant.Grav. 12 (1995) 2441-2468

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, REVTeX v3.0, 3 figures in a separate PostScript file

Scientific paper

10.1088/0264-9381/12/10/006

Witten's formulation of 2+1 gravity is investigated on the nonorientable three-manifold R x (Klein bottle). The gauge group is taken to consist of all four components of the 2+1 Poincare group. We analyze in detail several components of the classical solution space, and we show that from four of the components one can recover nondegenerate spacetime metrics. In particular, from one component we recover metrics for which the Klein bottles are spacelike. An action principle is formulated for bundles satisfying a certain orientation compatibility property, and the corresponding components of the classical solution space are promoted into a phase space. Avenues towards quantization are briefly discussed.

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