Manifolds that fail to be co-dimension 2 fibrators necessarily cover themselves

Abstract

Let N be a closed s-Hopfian n-manifold with residually finite, torsion free n^N) and finite H\(N). Suppose that either jr* (N) is finitely generated for all k > 2, or n k (N) = 0 for 1 < k < n -1, or n < 4. We show that if N fails to be a co-dimension 2 fibrator, then N cyclically covers itself, up to homotopy type.2000 Mathematics subject classification: primary 57N15, 55M25; secondary 57M10, 54B15.