Knot complements decomposing into prisms

2025/07/02 by Jason DeBlois, Arshia Gharagozlou, Deblois, Jason +3 · 1 voice
Mathematics · #57K10 #57K32 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2507.01263

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe four hyperbolic knot complements in \mathbbS³, each of which covers a prism orbifold: the quotient of ℍ³ 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.

Discussions

• It's about time I made a thread about a new paper from earlier this summer that constitutes a fairly major development, at least in the context of my little corner of mathematics. arxiv.org/abs/2507.0 [bsky, 7 points, 1 comments]

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