A semicontinuous trace for almost local operators on an open manifold
arXiv:math/0110294 · doi:10.1142/S0129167X01001106
Abstract
A semicontinuous semifinite trace is constructed on the C*-algebra generated by the finite propagation operators acting on the L^2-sections of a hermitian vector bundle on an amenable open manifold of bounded geometry. This trace is the semicontinuous regularization of a functional already considered by J. Roe. As an application, we show that, by means of this semicontinuous trace, Novikov-Shubin numbers for amenable manifolds can be defined (cf. math.OA/9802015 for an alternate definition).
17 pages, to appear on the International Journal of mathematics. This paper roughly correspond to the first section of the unpublished preprint math.DG/9809040