Geometry & Topology, Vol. 7 (2003)
Paper no. 7, pages 255--286.
Manifolds with non-stable fundamental groups at infinity, II
C R Guilbault and F C Tinsley
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.
Keywords.
End, tame, inward tame, open collar, pseudo-collar, semistable,
Mittag-Leffler, perfect group, perfectly semistable, Z-compactification
AMS subject classification.
Primary: 57N15, 57Q12.
Secondary: 57R65, 57Q10.
DOI: 10.2140/gt.2003.7.255
E-print: arXiv:math.GT/0304031
Submitted to GT on 6 September 2002.
Paper accepted 12 March 2003.
Paper published 31 March 2003.
Notes on file formats
C R Guilbault and F C Tinsley
Department of Mathematical Sciences, University of Wisconsin-Milwaukee
Milwaukee, Wisconsin 53201, USA
and
Department of Mathematics, The Colorado College
Colorado Springs, Colorado 80903, USA
Email: craigg@uwm.edu, ftinsley@cc.colorado.edu
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