Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Manifolds with non-stable fundamental groups at infinity, III

Craig R Guilbault and Frederick C Tinsley

Geometry & Topology 10 (2006) 541–556

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
References
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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