Hertz–Hertz–Ures weak dynamical coherence conjecture

Consider orientable 3-manifolds supporting partially hyperbolic dynamics. Hertz–Hertz–Ures weak dynamical coherence conjecture. The only orientable 3-manifolds supporting non-dynamically coherent dynamics are the 3-torus, the mapping torus of $-\operatorname{id}:\mathbb T^2\to\mathbb T^2$, and mapping tori of hyperbolic automorphisms of the 2-torus. This is the manifold-level consequence of the stronger torus-obstruction conjecture; the source marks the related strong conjecture as proved in the solvable-fundamental-group setting, but does not resolve this assertion generally.