Manifolds with non-stable fundamental groups at infinity

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 ( $n \geq 7$ ). 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

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

Craig R Guilbault
Department of Mathematical Sciences University of Wisconsin at Milwaukee Wisconsin 53201-0413 USA

Volume 4, issue 1 (2000)

Craig R Guilbault