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arxiv: 1706.03626 · v1 · pith:OLHZAK2Inew · submitted 2017-06-12 · 🧮 math.DS

On conservative partially hyperbolic abelian actions with compact center foliation

classification 🧮 math.DS
keywords actioncenterfoliationsmoothactionsanosovcompactconservative
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We consider smooth partially hyperbolic volume preserving Z^k actions on smooth manifolds, with uniformly compact center foliation. We show that under certain irreducibility condition on the action, bunching and uniform quasiconformality conditions, the action is a smooth fiber bundle extension of an Anosov action, or the center foliation is pathological. We obtain several corollaries of this result. For example, we prove a global dichotomy result that any smooth conservative circle extension over a maximal Cartan action is either essentially a product of an action by rotations and a linear Anosov action on the torus, or has a pathological center foliation.

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