Building on non-vanishing theorems of Kronheimer and Mrowka in instanton Floer homology, Zentner proved that if Y is a homology 3-sphere other than S^3, then its fundamental group admits a homomorphism to SL(2,C) with non-abelian image. In this talk, I’ll explain how to generalize this to any Y whose first homology is 2-torsion or 3-torsion, other than the connect sum of n copies of the three-dimensional real projective space for any n or lens spaces of order 3. This is joint work with Sudipta Ghosh and Raphael Zentner.