  Assuming it preserves an orientation of its stable bundle, any
three-dimensional partially hyperbolic diffeomorphism can be used to construct
a four-dimensional partially hyperbolic diffeomorphism which is dynamically
incoherent. Under the same assumption, the time-one map of any
three-dimensional Anosov flow can be used to construct a four-dimensional
diffeomorphism which is both absolutely partially hyperbolic and dynamically
incoherent. Further results hold in higher dimensions under additional
assumptions.
