Non-cobordant hyperbolic manifolds

Jacopo G. Chen

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arXiv · 2501.11610

Non-cobordant hyperbolic manifolds

Jacopo G. Chen

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Abstract

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 $4m+3 \ne 2^k-1$.

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BibTeX RIS

Jacopo G. Chen. 2025-01-20. Non-cobordant hyperbolic manifolds. https://arxiv.org/abs/2501.11610

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