# Poisson geometry of "SL" (3, C)-character varieties relative to a surface with boundary

@article{Lawton2007PoissonGO, title={Poisson geometry of "SL" (3, C)-character varieties relative to a surface with boundary}, author={Sean Lawton}, journal={Transactions of the American Mathematical Society}, year={2007}, volume={361}, pages={2397-2429} }

The SL(3, C)-representation variety R of a free group F r arises naturally by considering surface group representations for a surface with boundary. There is an SL(3,C)-action on the coordinate ring of R by conjugation. The geometric points of the subring of invariants of this action is an affine variety X. The points of X parametrize isomorphism classes of completely reducible representations. We show the coordinate ring C[X] is a complex Poisson algebra with respect to a presentation of F r…

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