2+1 GRAVITY FOR GENUS GREATER-THAN 1

In [1] we analysed the algebra of observables for the simple case of a genus 1 initial data surface SIGMA-2 for 2 + 1 De Sitter gravity. Here we extend the analysis to higher genus. We construct for genus 2 the group of automorphisms H of the homotopy group pi-1 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 for 6 threads.