We describe the geometry of the character variety of representations of the
knot group Γm,n=⟨x,y∣xn=ym⟩ into the group
SU(3), by stratifying the character variety into strata correspoding
to totally reducible representations, representations decomposing into a
2-dimensional and a 1-dimensional representation, and irreducible
representations, the latter of two types depending on whether the matrices have
distinct eigenvalues, or one of the matrices has one eigenvalue of multiplicity
2. We describe how the closure of each stratum meets lower strata, and use
this to compute the compactly supported Euler characteristic, and to prove that
the inclusion of the character variety for SU(3) into the character
variety for SL(3,C) is a homotopy equivalence.Comment: 22 pages, 4 figure