2 research outputs found
Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity
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).Comment: 34 pages, Mexico preprint ICN-UNAM-93-1