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  by dropping the assumption of dynamical coherence.
|Original language||English (US)|
|Number of pages||40|
|Journal||Journal of Modern Dynamics|
|State||Published - 2008|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics