Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914992218963968 |
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| author | Connell, Chris Ruan, Yuping Wang, Shi |
| author_facet | Connell, Chris Ruan, Yuping Wang, Shi |
| contents | We show that for any closed Riemannian manifold with dimension at least two and with nonpositive curvature, if it admits an isolated, closed totally geodesic submanifold of codimension one, then its simplicial volume is positive. As a direct corollary of this, for any nonpositively curved analytic manifold with dimension at least three, if its universal cover admits a codimension one flat, then either it has non-trivial Euclidean de Rham factors, or it has positive simplicial volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one Connell, Chris Ruan, Yuping Wang, Shi Geometric Topology Differential Geometry Primary 53C23, Secondary 57R19, 20F65 We show that for any closed Riemannian manifold with dimension at least two and with nonpositive curvature, if it admits an isolated, closed totally geodesic submanifold of codimension one, then its simplicial volume is positive. As a direct corollary of this, for any nonpositively curved analytic manifold with dimension at least three, if its universal cover admits a codimension one flat, then either it has non-trivial Euclidean de Rham factors, or it has positive simplicial volume. |
| title | Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one |
| topic | Geometric Topology Differential Geometry Primary 53C23, Secondary 57R19, 20F65 |
| url | https://arxiv.org/abs/2410.19981 |