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We continue our study of ends non-compact manifolds. The over-arching aim isto provide an appropriate generalization of Siebenmann's famous collaringtheorem that applies to manifolds having non-stable fundamental group systemsat infinity. In this paper a primary goal is finally achieved; namely, acomplete characterization of pseudo-collarability for manifolds of dimension atleast 6.Comment: This is the version published by Geometry & Topology on 27 April 200

Manifolds with non-stable fundamental groups at infinity, III