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

By Andy Hammerlindl, Rafael Potrie. 2013

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A classification of partially hyperbolic diffeomorphisms on three‐dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two‐dimensional torus, then it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures regarding dynamical coherence and leaf conjugacy in the specific case of solvable fundamental group.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a5e4e9deba5438907b6062a0a637794a1e510c1