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PreprintarXiv licencearXiv

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 ⊂ 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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Cite

BibTeXRIS
BibTeX
@misc{leininger2026filling,
  title = {{Filling knots and essential geodesic systole}},
  author = {Christopher J. Leininger and Yandi Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36259},
  eprint = {2610.36259},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36259},
}
RIS
TY  - UNPB
TI  - Filling knots and essential geodesic systole
AU  - Christopher J. Leininger
AU  - Yandi Wu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36259
UR  - https://arxiv.org/abs/2610.36259
AB  - 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 ⊂ 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.
ER  -