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arXiv · 2507.01263

Knot complements decomposing into prisms

Jason DeBlois·Arshia Gharagozlou·Neil R Hoffman
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Abstract

We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the combinatorial type of a triangular prism. The prism orbifolds are rigid-cusped and contain compact, totally geodesic hyperbolic triangle sub-orbifolds; as a result, the knot complements covering them have hidden symmetries and contain closed, embedded, totally geodesic surfaces.

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Jason DeBlois, Arshia Gharagozlou, Neil R Hoffman. 2026-03-26. Knot complements decomposing into prisms. https://arxiv.org/abs/2507.01263

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