Homotopy Groups And (2+1)-Dimensional Quantum Gravity

The integrated CCR (canonical commutation relations) for 2+1 dimensional gravity in the vielbein first order formalism are used to derive generalised representations Ψ: π1 (Σ) → ISO(2, 1) of the fundamental group of the initial data surface Σ2. The matrix elements of Ψ(U), Ψ(V), where U≠V are in general non-commuting according to a set of well-defined formal rules.