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Systoles of hyperbolic hybrids

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arxiv 2309.16051 v1 pith:73WSY7SU submitted 2023-09-27 math.GR math.GTmath.NT

Sami Douba This is my paper · ORCID
classification math.GRmath.GTmath.NT
keywords constructedhybridshyperbolicmanifoldsagolarbitrarilyauthorsbelolipetsky--thomson
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We exhibit closed hyperbolic manifolds with arbitrarily small systole in each dimension that are not quasi-arithmetic in the sense of Vinberg, and are thus not commensurable to those constructed by Agol, Belolipetsky--Thomson, and Bergeron--Haglund--Wise. This is done by taking hybrids of the manifolds constructed by the latter authors.

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  1. Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

    math.GT 2026-07 accept novelty 6.5 of 10

    For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.

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