Symplectic geometry of surface group representations
Symplectic geometry of surface group representations
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Bill Goldman, University of Maryland and IAS
In-Person Talk听
If G is a Lie group whose adjoint representation preserves a nondegenerate symmetric bilinear form on its Lie algebra (e.g. a semisimple group) and F is the fundamental group of a closed oriented surface S, then the spaces of equivalence classes of representations听 F-> G (equivalently gauge-equivalence classes of flat G-connections听over S) enjoys a rich symplectic geometry. These symplectic manifolds generalize the Kahler structures on the Jacobi variety, moduli of holomorphic vector bundles, and Teichmueller space. This talk will describe this geometry and several open questions about these symplectic manifolds.
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