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

J. E. Nelson·R. F. Picken
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Abstract

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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J. E. Nelson, R. F. Picken. 2005-01-20. Classical and quantum geometry of moduli spaces in three-dimensional gravity. https://arxiv.org/abs/math-ph/0501051

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