Geometry of SU(3)-character varieties of torus knots

We describe the geometry of the character variety of representations of the knot group Gamma m,n = (x, y|xn = ym) into the group SU(3), by stratifying the character va-riety into strata corresponding to totally reducible representations, representations decomposing into a 2-dimensional and a 1-dimensional representation, and irre-ducible 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.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).