Finding a boundary for a Hilbert cube manifold bundle (Q802174)

We develop an obstruction theory for the problem of determining whether a bundle, E, over a compact polyhedron, B, with non-compact Hilbert cube manifold fibers admits a boundary in the sense that there exists a compact bundle \(\bar E\) over B with Q-manifold fibers and a sliced Z-set, \(A\subset \bar E\), such that \(\bar E=A\cup E\). Included in the work is a new result on fibered weak proper homotopy equivalences, a theorem on proper liftings of homotopies, and the development of a sliced shape theory whose equivalences are shown to classify our boundaries through a tie to Q-manifold theory via a sliced version of Chapman's Complement Theorem.