Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
arXiv:math/0703251 · doi:10.1090/S0002-9947-08-04777-6
Abstract
The SL(3,C)-representation variety R of a free group F arises naturally by considering surface group representations for a surface with boundary. There is a 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 imposed by the surface. Lastly, we work out the bracket on all generators when the surface is a three-holed sphere or a one-holed torus.
33 pages, 11 figures, many revisions and some corrections, this version to appear in Transactions of the AMS
References in corpus (1)
Cited by in corpus (4)
- The topology of moduli spaces of free group representations
- Batalin-Vilkovisky structures on moduli spaces of flat connections
- Moduli spaces of real projective structures on surfaces: Notes on a paper by V.V. Fock and A.B. Goncharov
- Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus