Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

Details Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

1994-01-20

arxiv.org/abs/gr-qc/9401021v1

Phys.Rev. D50 (1994) 4966-4981

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, Mexico preprint ICN-UNAM-93-11

Scientific paper

10.1103/PhysRevD.50.4966

We establish the relation between the ISO(2,1) homotopy invariants and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2,1) cycle conditions, are equivalent to the ISO(2,1) cycle conditions for the representa- tions of the fundamental group in ISO(2,1). Also, the symplectic structure on the space of invariants is closely related to that of the polygon representation. We choose one of the polygon variables as internal time and compute the Hamiltonian, then perform the Hamilton-Jacobi transformation explicitly. We make contact with other authors' results for g = 1 and g = 2 (N = 0).

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