2+1 quantum gravity

In previous work we analysed the algebra of observables of the initial data surface Σ2 for 2+1 de Sitter gravity, and constructed for genus 2 the group of automorphisms H of the homotopy group π1 induced by the mapping class group. The group H induces a group D of canonical transformations on the algebra of observables which is related to the braid group. Here all of the previous results are implemented for any genus and at the quantum level.