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2+1 gravity for genus $$>1$$. (English) Zbl 0746.53062
Summary: In [Nucl. Phys. B 328, 190-202 (1989)] we analyzed 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.

##### MSC:
 53Z05 Applications of differential geometry to physics 83C47 Methods of quantum field theory in general relativity and gravitational theory
##### Keywords:
de Sitter gravity; algebra of observables; braid group
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##### References:
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