Manifolds with non-stable fundamental groups at infinity, III

Guilbault, Craig R; Tinsley, Frederick C

doi:10.2140/gt.2006.10.541

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Manifolds with non-stable fundamental groups at infinity, III

Craig R Guilbault and Frederick C Tinsley

Geometry & Topology 10 (2006) 541–556

DOI: 10.2140/gt.2006.10.541

arXiv: math.GT/0505517

Abstract

We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann’s famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete characterization of pseudo-collarability for manifolds of dimension at least 6.

Keywords

manifold, end, tame, inward tame, open collar, pseudo-collar, semistable, Mittag-Leffler, perfect group, perfectly semistable, Siebenmann's thesis, Wall finiteness obstruction, Quillen's plus construction

Mathematical Subject Classification 2000

Primary: 57N15, 57Q12

Secondary: 57R65, 57Q10

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Publication

Received: 24 May 2005

Accepted: 24 March 2006

Published: 27 April 2006

Proposed: Steven Ferry

Seconded: Benson Farb, Martin Bridson

Authors

Craig R Guilbault
Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI 53201 USA

Frederick C Tinsley
Department of Mathematics The Colorado College Colorado Springs Colorado 80903 USA

Volume 10, issue 1 (2006)