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}
}
  • S. Lawton
  • Published 9 March 2007
  • Mathematics
  • Transactions of the American Mathematical Society
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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