Simplicial volume of manifolds with amenable fundamental group at infinity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916495343222784 |
|---|---|
| author | Bargagnati, Giuseppe |
| author_facet | Bargagnati, Giuseppe |
| contents | 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 $π_1(M)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10525 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simplicial volume of manifolds with amenable fundamental group at infinity Bargagnati, Giuseppe Geometric Topology 57N16, 55N10 (Primary), 53C23, 57N65 (Secondary) 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 $π_1(M)$ 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. |
| title | Simplicial volume of manifolds with amenable fundamental group at infinity |
| topic | Geometric Topology 57N16, 55N10 (Primary), 53C23, 57N65 (Secondary) |
| url | https://arxiv.org/abs/2207.10525 |