Haken manifolds and representations of their fundamental groups in SL(2, C)

AbstractIt is shown in [2] that if the fundamental group of a compact orientable irreducible 3-manifold M has a positive-dimensional SL(2, C)-character variety, then M is a Haken manifold. We show however that the converse is not true. That is there exist infinitely many Haken manifolds whose fundamental groups have a finite number of representations in SL(2, C) up to equivalence. In particular, they have 0-dimensional SL(2, C)-character varieties