Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Leininger, Christopher J., Wu, Yandi
Institutions: University of Notre Dame, Rice University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224124133