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arXiv · 2610.36259

Filling knots and essential geodesic systole

Christopher J. Leininger·Yandi Wu
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Abstract

We prove that every closed, orientable $3$--manifold contains hyperbolic knots with arbitrarily large essential geodesic systole. That is, for any $3$--manifold $M$, and $R> 0$ there is a hyperbolic knot $K \subset M$ such that every closed geodesic in the knot complement which is non-null-homotopic in $M$ has length at least $R$. The construction also produces filling knots, in the sense of Freedman-Krushkal [FreeKrus2023]. This answers two questions of Biringer.

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BibTeXRIS

Christopher J. Leininger, Yandi Wu. 2026-10-26. Filling knots and essential geodesic systole. https://arxiv.org/abs/2610.36259

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