English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we continue the discussion of [6]. In §§1-3, we prove those results concerning the Von Neumann dimension of ZΛcohomology spaces (L Betti numbers) whose proofs were given only for normal coverings which are profinite. The ZΛcohomology techniques turn out to be useful in other contexts as well. For example, in [7] we simplify the proof of the theorem of Gottlieb and Stallings, which states that if a K{π, l)-space is homotopy equivalent to a finite complex and π has nontrivial center, then the Euler characteristic χ(ΛΓ(π, 1)) vanishes. In fact, we show that it suffices to assume that ΊT has a nontrivial normal amenable subgroup. In §4 we extend the result of [6] concerning the η-invariant to the not necessarily profinite case. For this we define a corresponding invariant τ/(2) by means of the Γ-trace. In §5 we extend our results to certain metrics which are conformally related to those considered in §1. We also give an intrinsic criterion (Theorem 5.5) for a metric to be of this type. As background for §§1-3 of the present paper, we now recall some material from [6]. There we considered a complete riemannian manifold M, whose sectional curvature, K, and volume, Vol(M), satisfy \K\ < 1, Vol(Λf) < oo. Here we will be concerned exclusively with the particular case in which

Bounds on the von Neumann dimension of $L\sp 2$-cohomology and the Gauss-Bonnet theorem for open manifolds