Manifolds with non-stable fundamental groups at infinity

Guilbault, Craig R¹

¹ Department of Mathematical Sciences, University of Wisconsin at Milwaukee, Wisconsin 53201-0413, USA

Geometry & topology, Tome 4 (2000) no. 1, pp. 537-579.

Résumé

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.

Détail

DOI : 10.2140/gt.2000.4.537

Keywords: non-compact manifold, ends, collar, homotopy collar, pseudo-collar, semistable, Mittag–Leffler

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