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arXiv · 2609.26663

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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Matthias Goerner, Robert C. Haraway III, Neil R. Hoffman, Maria Trnkova. 2026-09-22. Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds. https://arxiv.org/abs/2609.26663

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