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

Part of: Basic constructions Classical Topics in Algebraic Topology Low-dimensional topology Topological manifolds

Published online by Cambridge University Press:  09 April 2009

Young Ho Im  and
Yongkunk Kim
Young Ho Im
Affiliation:
Department of Mathematics Pusan National UniversityPusan 609–735Korea e-mail: yhim@pusan.ac.kr
Yongkunk Kim
Affiliation:
Department of Mathematics Kyungpook National UniversityTaegu 702–701Korea e-mail: yongkuk@knu.ac.kr
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Abstract

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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.

Keywords

residually finite groups-Hopfian manifoldapproximate fibration

MSC classification

Secondary: 57N15: Topology of $E^n$, $n$-manifolds ($4 less n less infty$) 55M25: Degree, winding number 57M10: Covering spaces 54B15: Quotient spaces, decompositions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 61 - 68
Copyright
Copyright © Australian Mathematical Society 2003

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