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

Abstract

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).

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

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• A Hamiltonian Formulation of Topological Gravity
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Cited by in corpus (4)

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• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Canonical Quantization of (2+1)-Dimensional Gravity
• $2+1$ Covariant Lattice Theory and t'Hooft's Formulation