Density of systoles of hyperbolic manifolds

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Abstract

We show that for each n 2, the systoles of closed hyperbolic n-manifolds form a dense subset of (0, +). We also show that for any n 2 and any Salem number, there is a closed arithmetic hyperbolic n-manifold of systole (). In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in (0, +).

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Douba et al. (Wed,) studied this question.

synapsesocial.com/papers/68e6de67b6db643587659efd https://doi.org/https://doi.org/10.48550/arxiv.2404.15927

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