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NECESSARY AND SUFFICIENT CONDITIONS FOR CODIMENSION-k MAPS TO BE APPROXIMATE FIBRATIONS

Im, Young-Ho

  • Published : 2003.04.01

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

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