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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.06362 |
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| _version_ | 1866910320220438528 |
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| author | Alpert, Hannah |
| author_facet | Alpert, Hannah |
| contents | We use Papasoglu's method of area-minimizing separating sets to give an alternative proof, and explicit constants, for the following theorem of Guth and Braun--Sauer: If $M$ is a closed, oriented, $n$-dimensional manifold, with a Riemannian metric such that every ball of radius $1$ in the universal cover of $M$ has volume at most $V_1$, then the simplicial volume of $M$ is at most the volume of $M$ times a constant depending on $n$ and $V_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06362 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simplicial volume and 0-strata of separating filtrations Alpert, Hannah Differential Geometry 53C23 We use Papasoglu's method of area-minimizing separating sets to give an alternative proof, and explicit constants, for the following theorem of Guth and Braun--Sauer: If $M$ is a closed, oriented, $n$-dimensional manifold, with a Riemannian metric such that every ball of radius $1$ in the universal cover of $M$ has volume at most $V_1$, then the simplicial volume of $M$ is at most the volume of $M$ times a constant depending on $n$ and $V_1$. |
| title | Simplicial volume and 0-strata of separating filtrations |
| topic | Differential Geometry 53C23 |
| url | https://arxiv.org/abs/2211.06362 |