Moduli spaces of flat connections and Morita equivalence of quantum tori

Details Moduli spaces of flat connections and Morita equivalence of quantum tori Moduli spaces of flat connections and Morita equivalence of quantum tori

2011-06-07

arxiv.org/abs/1106.1366v2

Mathematics

Symplectic Geometry

13 pages; v2: references added

Scientific paper

We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure (such as symplectic groupoid structure) gets a geometrical explanation via 3-dimensional cobordisms. We give a formula for the symplectic form in terms of holonomies, based on a central extension of the gauge group by closed 2-forms. This construction is finally used for a certain extension of the Morita equivalence of quantum tori to the world of Poisson-Lie groups.

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