Abstract: For a general class of 3-manifolds, the L^2-torsion of a manifold is a topological invariant that is determined by its simplicial volume. The idea of "twisting" is to use linear representations of the fundamental group to define more L^2-invariants. In this talk I will review the basic elements of L^2-torsion theory, and then show that the twisted L^2-torsion is a strictly positive function on the character variety. Moreover, this torsion function is continuous on the subvariety of upper triangular representations.
