Geometry & Topology 4 (2000) 537–579

DOI: 10.2140/gt.2000.4.537

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

Primary: 57N15, 57Q12

Secondary: 57Q10, 57R65

References

Forward citations

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