title:
Rigidity of pseudo-Anosov flows transverse to R-covered foliations


<p>

abstract:
Pseudo-Anosov flows are extremely common in three manifolds
and they are very useful. How many pseudo-Anosov flows are there
in a manifold up to topological conjugacy? We analyse how many such
flows there are transverse to a given foliation F. We prove that if
F is R-covered (leaf space in the universal cover is the real numbers) then there are at most two pseudo-Anosov flows transverse to F.
Usually there is at most one, but if there are two, then the foliation
F blows down to a foliation topologically conjugate to the stable
foliation of a particular type of an Anosov flow. The results
use the topological theory of pseudo-Anosov flows and the universal
cover for foliations.