Ends of Maps. II
In part I of this paper [Ann. Math., II. Ser. 110, 275-331 (1979; 394.57022)] the author shows that given a map f: \(M\to X\) with M a manifold, then a boundary can be added to M and the map extended to a proper map on the extended manifold provided that the end of f is tame, the local fundamental group is locally constant and satisfies \(Wh(\pi \times {\mathbb{Z}}^ n)=0\) for all n. In this paper the author relaxes the fundamental group hypothesis and develops a delicate obstruction theory - an \(\epsilon\)-version of C. T. C. Wall's finiteness obstruction. Although the proofs are artful and delicate, the obstructions tend to be practical to deal with. Several useful applications of this obstruction theory are given. For example obstructions to the triangulation of finite group actions and locally triangulable spaces are discussed. Also obstructions to approximating approximate fibrations by block bundles are presented.
equivariant mapping cylinder neighborhoods in topological group actions
scientific article; zbMATH DE number 3846481
scientific article