Von Neumann algebra invariants of Dirac operators (Q1379608)

A Novikov-Shubin invariant associated to the Dirac operator on \(L^2\)-spinors on the universal covering space of a compact Riemannian spin manifold is studied. This is a conformal invariant but it does depend on the conformal class. If this invariant is positive one can define the von Neumann algebra determinant of the Dirac Laplacian. A von Neumann algebra eta invariant associated to the Dirac operator provides in certain cases an obstruction to the existence of metrics of positive scalar curvature.