The complete $10$-tetrahedra census of orientable cusped hyperbolic $3$-manifolds

Shana Yunsheng Li

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arXiv · 2512.02142

The complete $10$-tetrahedra census of orientable cusped hyperbolic $3$-manifolds

Shana Yunsheng Li

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Abstract

We extend the complete census of orientable cusped hyperbolic $3$-manifolds to $10$ tetrahedra, giving the next $150730$ manifolds and their $496638$ minimal ideal triangulations. As applications, we find the precisely $439898$ exceptional Dehn fillings on them, revealing the next $1849$ simplest hyperbolic knot exteriors in $S^3$. We also give the simplest example of an orientable cusped hyperbolic $3$-manifold containing a closed totally geodesic surface.

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Shana Yunsheng Li. 2025-12-01. The complete $10$-tetrahedra census of orientable cusped hyperbolic $3$-manifolds. https://arxiv.org/abs/2512.02142

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