Analytic torsion on manifolds under locally compact group actions (Q2509819)

In this paper the author defines the analytic torsion on a complete Riemannian manifold without boundary where a unimodular locally compact group properly cocompact acts on it. To do that the author uses some similar conditions as the Novikov-Shubin invariants. Then the author proves an anomaly formula for the analytic torsion. This formula shows that the analytic torsion does not depend on the Riemannian metric in the case that the dimension of the space is odd and the \(L^2\)-cohomology is trivial. In the end, using techniques from \textit{J. L. Heitsch} and \textit{C. Lazarov} [J. Geom. Anal. 12, No. 3, 437--468 (2002; Zbl 1032.58017)], the author defines the torsion form for a fiber bundle \(\pi: M \to B\) with a unimodular locally compact group properly cocompact fiberwisely acting on it and shows that the \(0\)-degree part of the torsion form is equal to the analytic torsion.