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PreprintarXiv licencearXiv

Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds

  • Matthias Goerner
  • Robert C. Haraway III
  • Neil R. Hoffman
  • Maria Trnkova
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Abstract

We present a new algorithm to compute a stream for the length spectrum of an oriented, finite-volume hyperbolic 3-manifold M. The advantage over the existing algorithm by Hodgson-Weeks is that our algorithm does not require finding a Dirichlet domain and thus can use interval arithmetic to verify the result. Our algorithm is also significantly faster in some cases. We also present a new algorithm to compute the optimal Margulis number of M. The authors have made these algorithms available in SnapPy.

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Cite

BibTeXRIS
BibTeX
@misc{goerner2026verified,
  title = {{Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds}},
  author = {Matthias Goerner and Robert C. Haraway III and Neil R. Hoffman and Maria Trnkova},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26663},
  eprint = {2609.26663},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26663},
}
RIS
TY  - UNPB
TI  - Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds
AU  - Matthias Goerner
AU  - Robert C. Haraway III
AU  - Neil R. Hoffman
AU  - Maria Trnkova
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26663
UR  - https://arxiv.org/abs/2609.26663
AB  - We present a new algorithm to compute a stream for the length spectrum of an oriented, finite-volume hyperbolic 3-manifold M. The advantage over the existing algorithm by Hodgson-Weeks is that our algorithm does not require finding a Dirichlet domain and thus can use interval arithmetic to verify the result. Our algorithm is also significantly faster in some cases. We also present a new algorithm to compute the optimal Margulis number of M. The authors have made these algorithms available in SnapPy.
ER  -