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On the positivity of twisted $L^2$-torsion for 3-manifolds (2209.10145v1)
Published 21 Sep 2022 in math.GT
Abstract: For any compact orientable irreducible 3-manifold $N$ with empty or incompressible toral boundary, the twisted $L2$-torsion is a non-negative function defined on the representation variety $\operatorname{Hom}(\pi_1(N),\operatorname{SL}(n,\mathbb C))$. The paper shows that if $N$ has infinite fundamental group, then the $L2$-torsion function is strictly positive. Moreover, this torsion function is continuous when restricted to the subvariety of upper triangular representations.