Non-cobordant hyperbolic manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916574548459520 |
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| author | Chen, Jacopo G. |
| author_facet | Chen, Jacopo G. |
| contents | In all dimensions $n \ge 4$ not of the form $4m+3$, we show that there exists a closed hyperbolic $n$-manifold which is not the boundary of a compact $(n+1)$-manifold. The proof relies on the relationship between the cobordism class and the fixed point set of an involution on the manifold, together with a geodesic embedding of Kolpakov, Reid and Slavich. We also outline a possible approach to cover the dimensions $4m+3 \ne 2^k-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-cobordant hyperbolic manifolds Chen, Jacopo G. Geometric Topology In all dimensions $n \ge 4$ not of the form $4m+3$, we show that there exists a closed hyperbolic $n$-manifold which is not the boundary of a compact $(n+1)$-manifold. The proof relies on the relationship between the cobordism class and the fixed point set of an involution on the manifold, together with a geodesic embedding of Kolpakov, Reid and Slavich. We also outline a possible approach to cover the dimensions $4m+3 \ne 2^k-1$. |
| title | Non-cobordant hyperbolic manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2501.11610 |