Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary

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dc.creatorLawton, Sean
dc.date2007-03-09
dc.date2008-03-03
dc.date.accessioned2026-07-07T12:52:31Z
dc.date.available2026-07-07T12:52:31Z
dc.descriptionThe 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.
dc.description33 pages, 11 figures, many revisions and some corrections, this version to appear in Transactions of the AMS
dc.identifierhttps://arxiv.org/abs/math/0703251
dc.identifierhttp://arxiv.org/abs/math/0703251
dc.identifierTrans. Amer. Math. Soc. 361 (2009), 2397-2429
dc.identifierdoi:10.1090/S0002-9947-08-04777-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223317
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.subject58D29; 14D20
dc.titlePoisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
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