Irreducible Components in an Algebraic Variety of Representations of a Family of One-relator Groups
نویسنده
چکیده
Given a finitely generated group G, the set Hom(G, SL2C) inherits the structure of an algebraic variety R(G) called the representation variety of G. This algebraic variety is an invariant of G. Let Gpt = 〈a, b; a p = b〉, where p, t are integers greater than one. In this paper a formula is produced yielding the number of four dimensional irreducible components of the affine algebraic variety R(Gpt). A direct consequence of the main theorem of this paper is that if K is a torus knot, then its genus equals the number of four dimensional components of the representation variety, R(Gpt), of its corresponding knot group Gpt.
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