Geometry Seminar - Abstracts


Thursday 13 October 2016, 16:00 - 17:00, in tba
Victor Mouquin (University of Toronto)
The Fock-Rosly Poisson structure and quasi-triangular r-matrices


The moduli space of flat $G$-connections over a Riemann surface $\Sigma$ is well known to admit a natural Poisson structure. If one looks at principal $G$-bundles trivialized over finitely many points $v_1, ..., v_n$ lying in the boundary of $\Sigma$, Fock and Rosly have constructed a Poisson structure on the corresponding moduli space of flat connections which depends on the choice of an $r$-matrix for each point $v_j$. We show that this Fock-Rosli Poisson structure is defined by a quasitriangular $r$-matrix, and is an example of fusion of Poisson spaces

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