Homotopy groups and (2 + 1)-dimensional quantum de Sitter gravity

The integrated CCR (canonical commutation relations) for (2 + 1)- dimensional de Sitter/ anti-de Sitter gravity in first-order formalism are used to derive generalised spinor representations of the fundamental group of the initial data surface Σ2. The matrix elements of Ψ(U), Ψ(V), with U ≠ V are in general non-commuting according to a set of formal rules which are related to the theory of quantum groups. The Poincaré theory appears as a limiting case.