English

Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

Dynamical Systems 2025-06-03 v1

Abstract

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic, giving an affirmative answer to the Hertz-Hertz-Ures Ergodicity Conjecture in the homotopy class of identity.

Keywords

Cite

@article{arxiv.2506.00405,
  title  = {Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three},
  author = {Ziqiang Feng and Raúl Ures},
  journal= {arXiv preprint arXiv:2506.00405},
  year   = {2025}
}

Comments

41 pages. This is a preliminary version