Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups

Dmitri Burago, Sergei Ivanov

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Abstract

We present the first known nontrivial topological obstructions to the existence of partially hyperbolic diffeomorphisms. In particular, we show that there are no partially hyperbolic diffeomorphisms on the 3-sphere. More generally, we show that for a partially hyperbolic diffeomorphismof a 3-manifoldwith an Abelian fundamental group, the induced action in the first homology group is partially hyperbolic. This improves the results of [4] by dropping the assumption of dynamical coherence.

Original languageEnglish (US)
Pages (from-to)541-580
Number of pages40
JournalJournal of Modern Dynamics
Volume2
Issue number4
DOIs
Publication statusPublished - Dec 1 2008

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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