Algebraic geometric invariants for a class of one-relator groups Original Research Article

Given a finitely generated group H, the set Hom(H, SL2C) inherits the structure of an affine algebraic variety R(H) called the representation variety of H. Let a one-relator group with presentation image be given, where image is in the free group on the generators image, and k ≥ 2. In this paper a theorem will be proven allowing the computation of Dim(R(G)) in terms of subvarieties of the representation variety of the free group on n generators, R(Fn), arising from solutions to the equation image in SL2C. Conditions are given guaranteeing the reducibility of R(G). Finally, applications to the class of one-relator groups with non-trivial center are made.