Strong Ergodicity Conjecture for partially hyperbolic diffeomorphisms on 3-manifolds

Let $f$ be a $C^r$ ($r>1$) conservative partially hyperbolic diffeomorphism on a 3-manifold, with invariant bundles $E^s$ and $E^u$. Strong Ergodicity Conjecture. If $f$ is non-ergodic, then there exists an embedded 2-torus tangent to $E^s\oplus E^u$. The conjecture is presented as a stronger form of the preceding ergodicity conjecture and as asserting that the obstruction to ergodicity is a proper compact accessibility class; its status is not resolved in the supplied text.