Simplicial volume of manifolds with amenable fundamental group at infinity

Abstract

We show that for $n\ne 1,4$ 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.

11 pages

References in corpus (3)

• Manifolds with non-stable fundamental groups, at infinity
• Manifolds with non-stable fundamental groups at infinity, II
• Isomorphisms in l^1-homology