Foliated control with hyperbolic leaves

The main result is a control theorem for the space of stable pseudo-isotopies on E with control near the leaves of F in M, where : E M is a fiber bundle over the compact closed Riemannian manifold M having a compact manifold for fiber and F is a smooth foliation of M. The proof of this foliated control result combines the (unfoliated) control results of 14] with the long and thin cell structures and the asymptotic transfer of 6] and 7].Both authors were supported in part by the NSF.