Delooping controlled pseudo-isotopies of Hilbert cube manifolds

Abstract

This paper is concerned with the controlled simple homotopy theory and controlled pseudo-isotopy theory of a Hurewicz fibration p: E→ B from a compact Hilbert cube manifold E to a compact polyhedron B. The main result is that the controlled pseudo-isotopy space is homotopy equivalent to the loop space of the controlled Whitehead space.