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Symmetries in the SL(3, C)-Character Variety of a Rank 2 Free Group
by
Sean Lawton
University of Maryland
Denote the free group on two letters by F2 and the SL(3, C)-representation variety of F2 by R=Hom(F2, SL(3, C)). There is a SL(3, C)-action on the coordinate ring of R, and the geometric points of the subring of invariants is an affine variety X. It is has been shown by A. Sikora that X corresponds to the SU(3)-skein module of a 3-manifold with fundamental group F2. We determine explicit minimal generators for the subring of invariants which exhibit Out(F2) symmetries and allow for a succinct expression of the defining relations.
Date received: April 27, 2006
Copyright © 2006 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # casv-13.