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2003 Manifolds with non-stable fundamental groups at infinity, II
Craig R Guilbault, Frederick C Tinsley
Geom. Topol. 7(1): 255-286 (2003). DOI: 10.2140/gt.2003.7.255

Abstract

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.

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Craig R Guilbault. Frederick C Tinsley. "Manifolds with non-stable fundamental groups at infinity, II." Geom. Topol. 7 (1) 255 - 286, 2003. https://doi.org/10.2140/gt.2003.7.255

Information

Received: 6 September 2002; Accepted: 12 March 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1032.57020
MathSciNet: MR1988286
Digital Object Identifier: 10.2140/gt.2003.7.255

Subjects:
Primary: 57N15, 57Q12
Secondary: 57Q10, 57R65

Rights: Copyright © 2003 Mathematical Sciences Publishers

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Vol.7 • No. 1 • 2003
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