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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.

53Z05 Applications of differential geometry to physics
83C47 Methods of quantum field theory in general relativity and gravitational theory
Full Text: DOI
[1] Nelson, J.E., Regge, T.: Nucl. Phys. B328, 190 (1989) · doi:10.1016/0550-3213(89)90099-0
[2] Nelson, J.E., Regge, T., Zertuche, F.: Nucl. Phys. B339, 516 (1990) · doi:10.1016/0550-3213(90)90359-L
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[7] Carlip, S.: Time in 2+1 dimensional quantum gravity. Proc. Banff Conference on Gravitation, Canada 1990; and Moncrief, V.: J. Math. Phys.30, 12 (1989)
[8] Nelson, J.E., Regge, T.: In preparation
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