Manifolds with non-stable fundamental groups, at infinity

Abstract

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 > 6). 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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper19.abs.html

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• Simplicial volume of manifolds with amenable fundamental group at infinity
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• $\mathcal{Z}$-compactifiable manifolds which are not pseudo-collarable