A semicontinuous trace for almost local operators on an open manifold
Differential Geometry
2007-05-23 v1 Operator Algebras
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).
Cite
@article{arxiv.math/0110294,
title = {A semicontinuous trace for almost local operators on an open manifold},
author = {Daniele Guido and Tommaso Isola},
journal= {arXiv preprint arXiv:math/0110294},
year = {2007}
}
Comments
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 This paper roughly correspond to the first section of the unpublished preprint math.DG/9809040