\(L^ 2\)-analytic torsion (Q1193916)

The author introduces a new differential invariant called \(L^ 2\)- analytic torsion, for closed manifolds whose universal covers have trivial \(L^ 2\)-cohomology, under the conjecture that these manifolds have positive decay. This means that the von Neumann trace of the heat kernel of the Laplacian minus the harmonic projection on \(L^ 2\) \(j\)- forms decays faster than some negative power of time. Various functional properties of \(L^ 2\)-analytic torsion are established and some explicit calculations of this invariant are made.