Geometry & Topology, Vol. 4 (2000) Paper no. 19, pages 537--579.

Manifolds with non-stable fundamental groups at infinity

Craig R Guilbault

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 > 6). 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

AMS subject classification. Primary: 57N15, 57Q12. Secondary: 57R65, 57Q10.

DOI: 10.2140/gt.2000.4.537

E-print: arXiv:math.GT/0101030

Submitted to GT on 30 July 1999. (Revised 8 December 2000.) Paper accepted 27 December 2000. Paper published 27 December 2000.

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Craig R Guilbault
Department of Mathematical Sciences
University of Wisconsin-Milwaukee
WI 53201-0413, USA
Email: craigg@uwm.edu

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