In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic $4$-manifold of finite volume and give some partial results on the "geography" of such manifolds. The main ingredients are a theorem of Long and Reid, and the explicit construction of a hyperbolic 24-cell manifold with some special topological properties.Few things are harder to put up with than the annoyance of a good example.- Mark Twain
The Signature of Cusped Hyperbolic 4-Manifolds / Alexander Kolpakov; Stefano Riolo; Steven T Tschantz. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2023:9(2023), pp. 7961-7975. [10.1093/imrn/rnac227]
The Signature of Cusped Hyperbolic 4-Manifolds
Stefano Riolo;
2023
Abstract
In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic $4$-manifold of finite volume and give some partial results on the "geography" of such manifolds. The main ingredients are a theorem of Long and Reid, and the explicit construction of a hyperbolic 24-cell manifold with some special topological properties.Few things are harder to put up with than the annoyance of a good example.- Mark Twain| File | Dimensione | Formato | |
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