Asimptotic dimension and Novikov-Shubin invariants for open manifolds
| dc.creator | Guido, D. | |
| dc.creator | Isola, T. | |
| dc.date | 1996-12-23 | |
| dc.date.accessioned | 2026-07-07T09:12:56Z | |
| dc.date.available | 2026-07-07T09:12:56Z | |
| dc.description | A trace on the C^*-algebra A of quasi-local operators on an open manifold is described, based on the results in \cite{RoeOpen}. It allows a description `a la Novikov-Shubin \cite{NS2} of the low frequency behavior of the Laplace-Beltrami operator. The 0-th Novikov-Shubin invariant defined in terms of such a trace is proved to coincide with a metric invariant, which we call asymptotic dimension, thus giving a large scale ``Weyl asymptotics'' relation. Moreover, in analogy with the Connes-Wodzicki result \cite{CoCMP,Co,Wo}, the asymptotic dimension d measures the singular traceability (at 0) of the Laplace-Beltrami operator, namely we may construct a (type II_1) singular trace which is finite on the $^*$-bimodule over A generated by $Δ^{-d/2}$. | |
| dc.description | LaTeX2e, 39 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9612015 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9612015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152195 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 58-XX (Primary) 46Lxx (Secondary) | |
| dc.title | Asimptotic dimension and Novikov-Shubin invariants for open manifolds | |
| dc.type | text |