Geodesic
Moduli spaces of flat connections and Morita equivalence of quantum tori
Documenta mathematica, Tome 17 (2012), pp. 607-625
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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.
DOI : 10.4171/dm/377
Classification : 53D30 
@article{10_4171_dm_377,
     author = {Pavol Severa},
     title = {Moduli spaces of flat connections and {Morita} equivalence of quantum tori},
     journal = {Documenta mathematica},
     pages = {607--625},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/377},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/377/}
}
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Pavol Severa. Moduli spaces of flat connections and Morita equivalence of quantum tori. Documenta mathematica, Tome 17 (2012), pp. 607-625. doi: 10.4171/dm/377

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