  Using deformations of foliations to contact structures as well as rigidity
properties of Anosov foliations we provide infinite families of examples which
show that the space of taut foliations in a given homotopy class of plane
fields is in general not path connected. Similar methods also show that the
space of representations of the fundamental group of a hyperbolic surface to
the group of smooth diffeomorphisms of the circle with fixed Euler class is in
general not path connected. As an important step along the way we resolve the
question of which universally tight contact structures on Seifert fibered
spaces are deformations of taut or Reebless foliations when the genus of the
base is positive or the twisting number of the contact structure in the sense
of Giroux is non-negative.
