Certifying fibredness and hyperbolicity of 3-manifolds

Filippo Baroni discusses the computational complexity of two questions about a given 3-manifold: does it fibre over the circle, and if it does, is it hyperbolic? Deciding fibredness lies in NP, so a positive answer can be certified efficiently, slightly generalising a theorem of Saul Schleimer. Hyperbolicity of a fibred 3-manifold can also be certified efficiently, though not quite enough to place that problem in NP. Combined with a recently announced theorem of Marc Lackenby, these results show that deciding whether a knot in the 3-sphere is hyperbolic lies in NP. The talk is based on the preprint arXiv:2606.23284.