Manifolds with non-stable fundamental groups at infinity, II

Guilbault, Craig R¹ ; Tinsley, Frederick C²

¹ Department of Mathematical Sciences, University of Wisconsin at Milwaukee, Milwaukee, Wisconsin 53201, USA
² Department of Mathematics, The Colorado College, Colorado Springs, Colorado 80903, USA

Geometry & topology, Tome 7 (2003) no. 1, pp. 255-286.

Résumé

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann’s famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with compact boundary, the condition of inward tameness has substatial implications for the algebraic topology at infinity. In particular, every inward tame manifold with compact boundary has stable homology (in all dimensions) and semistable fundamental group at each of its ends. In contrast, we also construct examples of this sort which fail to have perfectly semistable fundamental group at infinity. In doing so, we exhibit the first known examples of open manifolds that are inward tame and have vanishing Wall finiteness obstruction at infinity, but are not pseudo-collarable.

Détail

DOI : 10.2140/gt.2003.7.255

Keywords: end, tame, inward tame, open collar, pseudo-collar, semistable, Mittag-Leffler, perfect group, perfectly semistable, Z-compactification

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