Abstract
Abstract
We show that for
$n \neq 1,4$
, the simplicial volume of an inward tame triangulable open
$n$
-manifold
$M$
with amenable fundamental group at infinity at each end is finite; moreover, we show that if also
$\pi _1(M)$
is amenable, then the simplicial volume of
$M$
vanishes. We show that the same result holds for finitely-many-ended triangulable manifolds which are simply connected at infinity.
Publisher
Cambridge University Press (CUP)
Reference20 articles.
1. The fundamental group at infinity
2. [17] Perelman, G. , Ricci flow with surgery on three-manifolds. arXiv: math/0303109.
3. Isomorphisms in
$l^1$
-homology;Löh;Münster J. Math.,2008
4. Geometrisation of 3-Manifolds
5. Manifolds with non-stable fundamental groups at infinity