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

• Published in: Journal of the Australian Mathematical Society (2001) Vol. 74; no. 1; pp. 61 - 68
• Main Authors: Im, Young Ho, Kim, Yongkunk
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.02.2003
• Subjects: 54B15; 55M25; approximate fibration; primary 57N15; residually finite group; s-Hopfian manifold; secondary 57M10; secondary 57M10; 55M25; 54B15; s-Hopfian manifold; primary 57N15; approximate fibration; residually finite group
• ISSN: 1446-7887; 1446-8107
• DOI: 10.1017/S1446788700003128

Let N be a closed s-Hopfian n-manifold with residually finite, torsion free π1 (N) and finite H1(N). Suppose that either πk(N) is finitely generated for all k ≥ 2, or πk(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.