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Simplicial volume of manifolds with amenable fundamental group at infinity
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- Journal:
- Glasgow Mathematical Journal / Volume 66 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 22 April 2024, pp. 563-570
- Print publication:
- September 2024
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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.
Topological volumes of fibrations: a note on open covers
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 5 / October 2022
- Published online by Cambridge University Press:
- 11 October 2021, pp. 1340-1360
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- October 2022
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MINIMAL VOLUME OF COMPLETE UNIFORM VISIBILITY MANIFOLDS WITH FINITE VOLUME
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- Journal:
- Journal of the Australian Mathematical Society / Volume 94 / Issue 3 / June 2013
- Published online by Cambridge University Press:
- 07 June 2013, pp. 375-384
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- June 2013
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We show that complete uniform visibility manifolds of finite volume with sectional curvature
$- 1\leq K\leq 0$ have positive simplicial volume. This implies that their minimal volume is nonzero.
