Necessary and sufficient conditions for codimension-$k$ maps to be approximate fibrations
Commun. Korean Math. Soc. 2003 Vol. 18, No. 2, 367-374
Printed June 1, 2003
Young Ho Im
Pusan National University
Abstract : Let $N$ be a closed $n$-manifold with residually finite, torsion free $\pi_1(N)$ and finite $H_1(N)$. Suppose that $\pi_k(N)=0$ for $1 < k < n-1$. We show that $N$ is a codimension-$n$ PL fibrator if and only if $N$ does not cover itself regularly and cyclically up to homotopy type, provided $\pi_1(N)$ satisfies a certain condition.
Keywords : residually finite group; hopfian manifold; approximate fibration
MSC numbers : Primary 57N15, 55M25; Secondary 57M10, 54B15
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