Volume 4, issue 1 (2000)

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

Craig R Guilbault

Geometry & Topology 4 (2000) 537–579

arXiv: math.GT/0101030

Abstract

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n–manifold (n 7). This paper may be viewed as a generalization of Siebenmann’s famous collaring theorem to open manifolds with non-stable fundamental group systems at infinity.

Keywords
non-compact manifold, ends, collar, homotopy collar, pseudo-collar, semistable, Mittag–Leffler
Mathematical Subject Classification 2000
Primary: 57N15, 57Q12
Secondary: 57R65, 57Q10
References
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Publication
Received: 30 July 1999
Revised: 8 December 2000
Accepted: 27 December 2000
Published: 27 December 2000
Proposed: Steve Ferry
Seconded: Robion Kirby, Cameron Gordon
Authors
Craig R Guilbault
Department of Mathematical Sciences
University of Wisconsin at Milwaukee
Wisconsin 53201-0413
USA