We show that for n ≠ 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 π1(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.
Bargagnati, G. (2024). Simplicial volume of manifolds with amenable fundamental group at infinity. GLASGOW MATHEMATICAL JOURNAL, 66(3), 563-570 [10.1017/s0017089524000107].
Simplicial volume of manifolds with amenable fundamental group at infinity
Bargagnati, Giuseppe
2024
Abstract
We show that for n ≠ 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 π1(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.File in questo prodotto:
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