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 \(\rho\) : \(E\to M\) 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 \textit{F. Quinn} [Invent. Math. 68, 353-424 (1982; Zbl 0533.57008)] with the `long and thin' cell structures and the `asymptotic transfer' of the authors' papers: ``K-theory and dynamics. I, II'' [Ann. Math., II. Ser. 124, 531-569 (1986; Zbl 0653.58035) and ibid. 126, 451- 493 (1987)].
scientific article; zbMATH DE number 4076086