Three-manifolds that do not admit veering triangulations

Layne Hall

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arXiv · 2610.37057

Three-manifolds that do not admit veering triangulations

Layne Hall

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Abstract

We show that if a three-manifold $M$ admits a veering triangulation, then the dual spine of every essential triangulation of $M$ can be smoothed to a branched surface. We use this criterion to identify a large collection of cusped hyperbolic three-manifolds that do not admit veering triangulations. We then use the same criterion to construct the first infinite family of cusped hyperbolic three-manifolds without veering triangulations.

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Layne Hall. 2026-10-27. Three-manifolds that do not admit veering triangulations. https://arxiv.org/abs/2610.37057

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