Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group

Abstract

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures by Rodriguez Hertz--Rodriguez Hertz--Ures and Pujals in the specific case of solvable fundamental group.

36 pages, 3 figures. To appear in the Journal of Topology

References in corpus (3)

• Pointwise partial hyperbolicity in 3-dimensional nilmanifolds
• Partial hyperbolicity and attracting regions in 3-dimensional manifolds
• A non-dynamically coherent example on ${\mathbb{T}}^3$

Cited by in corpus (14)

• Partial hyperbolicity and classification: a survey
• Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence
• Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples
• A few remarks on partially hyperbolic diffeomorphisms of ${\mathbb{T}}^3$ isotopic to Anosov
• Rigidity of some abelian-by-cyclic solvable group actions on ${\mathbb{T}}^N$
• Partially hyperbolic surface endomorphisms
• Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center
• Partially hyperbolic dynamics in dimension 3
• Integrability of dominated decompositions on three-dimensional manifolds
• Constructing center-stable tori
• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations
• Accessibility of derived-from-Anosov systems
• $C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle
• An answer to Hammerlindl's question on strong unstable foliations