Ends of Maps. II
type: Item
instance of: scholarly article
title: Ends of Maps. II
zbMATH Open document ID: 0533.57008
DOI: 10.1007/BF01389410
author: Frank Quinn
published in: Inventiones Mathematicae
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/142938
review text: 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.
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 57N55
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57Q10
Mathematics Subject Classification ID: 57Q12
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 57Q40
Mathematics Subject Classification ID: 57N80
zbMATH DE Number: 3846481
zbMATH Keywords: s-cobordism
zbMATH Keywords: equivariant mapping cylinder neighborhoods in topological group actions
zbMATH Keywords: end of maps
zbMATH Keywords: simple homotopy theory
zbMATH Keywords: 394.57022
zbMATH Keywords: finiteness obstruction
zbMATH Keywords: triangulation
zbMATH Keywords: locally triangulable spaces
zbMATH Keywords: approximate fibrations
zbMATH Keywords: block bundles
reviewed by: R. J. Stern
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3846481