On the positivity of twisted $L^2$-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 $\mathrm{Hom}({\pi }_1(N),\mathrm{SL}(n,\mathbb{C}))$. 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.