We use instanton gauge theory to prove that if Y Y is a closed, orientable 3 3 -manifold such that H 1 (Y ; Z) H₁ (Y; Z) is nontrivial and either 2 2 -torsion or 3 3 -torsion, and if Y Y is neither # r R P 3 \#^r RP^3 for some r ≥ 1 r 1 nor ± L (3, 1) L (3, 1), then there is an irreducible representation π 1 (Y) → SL (2, C) ₁ (Y) SL (2, C). We apply this to show that the Kauffman bracket skein module of a non-prime 3-manifold has nontrivial torsion whenever two of the prime summands are different from R P 3
Ghosh et al. (Fri,) studied this question.