2011/06/07 by Pavol Ševera, Ševera, Pavol
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1106.1366
openalex publication_date 2011/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.