One way to effectively show a group is non-trivial is to find a non-trivial representation.  A major open question in low-dimensional topology is whether the fundamental group of a closed three-manifold other than S^3 has a non-trivial SU(2) representation, and this is a strategy for an alternate proof of the three-dimensional Poincare conjecture.  We will show that every homology three-sphere with an essential torus admits such a representation.  This is joint work with Juanita Pinzon-Caicedo and Raphael Zentner.