Geometry & Topology

Manifolds with non-stable fundamental groups at infinity, III

Craig R Guilbault and Frederick C Tinsley

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We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann’s famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete characterization of pseudo-collarability for manifolds of dimension at least 6.

Article information

Geom. Topol., Volume 10, Number 1 (2006), 541-556.

Received: 24 May 2005
Accepted: 24 March 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N15: Topology of $E^n$ , $n$-manifolds ($4 \less n \less \infty$) 57Q12: Wall finiteness obstruction for CW-complexes
Secondary: 57R65: Surgery and handlebodies 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]

manifold end tame inward tame open collar pseudo-collar semistable Mittag-Leffler perfect group perfectly semistable Siebenmann's thesis Wall finiteness obstruction Quillen's plus construction


Guilbault, Craig R; Tinsley, Frederick C. Manifolds with non-stable fundamental groups at infinity, III. Geom. Topol. 10 (2006), no. 1, 541--556. doi:10.2140/gt.2006.10.541.

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