Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points

We prove that every C² conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold M with no periodic points is accessible if the non-wandering set is all of M and the fundamental group ₁ (M) is not virtually solvable.