J. Aust. Math. Soc.  74 (2003), 61-67
Manifolds that fail to be co-dimension 2 fibrators necessarily cover themselves

Young Ho Im
  Department of Mathematics
  Pusan National University
  Pusan 609-735
  Korea
  yhim@pusan.ac.kr
and
Yongkuk Kim
  Department of Mathematics
  Kyungpook National University
  Taegu 702-701
  Korea
  yongkuk@knu.ac.kr


Abstract
Let $N$ be a closed s-Hopfian $n$-manifold with residually finite, torsion free $\pi_1(N)$ and finite $H_1(N)$. Suppose that either $\pi_k(N)$ is finitely generated for all $k \geq 2$, or $\pi_k(N) \cong 0$ for $1 < k < n-1$, or $n \leq 4$. We show that if $N$ fails to be a co-dimension 2 fibrator, then $N$ cyclically covers itself, up to homotopy type.
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