Classical and quantum geometry of moduli spaces in three-dimensional gravity

Details Classical and quantum geometry of moduli spaces in three-dimensional gravity Classical and quantum geometry of moduli spaces in three-dimensional gravity

2005-01-20

arxiv.org/abs/math-ph/0501051v1

Physics

Mathematical Physics

12 pages, including contents page (proceedings format), submitted to the Proceedings of the XIII Fall Workshop on Geometry and

Scientific paper

We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to parametrise the geometry. After quantization, these matrices acquire non-commuting entries, in such a way that they satisfy q-commutation relations and exhibit interesting geometrical properties. In particular they lead to a quantization of the Goldman bracket.

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