On the positivity of twisted L2–torsion for 3–manifolds

For any compact orientable irreducible 3-manifold N with empty or incompressible toral boundary, the twisted L 2 -torsion is a non-negative function defined on the representation variety Hom(π 1 (N ), SL(n, C)).The paper shows that if N has infinite fundamental group, then the L 2 -torsion function is strictly positive.Moreover, this torsion function is continuous when restricted to the subvariety of upper triangular representations.