#### Volume 4, issue 1 (2000)

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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 ($n\ge 7$). 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