Integrability of dominated decompositions on three-dimensional manifolds

Stefano Luzzatto, Sina Tureli, Khadim War

Published 2014-10-29Version 1

We prove that, under some mild transverse regularity assumptions,dominated distributions on three-dimensional manifolds are integrable. We also give conditions for unique integrability and as an immediate corollary we get that every partially hyperbolic C^{2} diffeomorphism on a three-dimensional manifold whose tangent bundle decomposition satisfies a weak regularity condition is dynamically coherent.