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arXiv · 1106.1366

Moduli spaces of flat connections and Morita equivalence of quantum tori

Pavol Ševera
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Abstract

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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Pavol Ševera. 2011-06-16. Moduli spaces of flat connections and Morita equivalence of quantum tori. https://arxiv.org/abs/1106.1366

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