Communications of the
Korean Mathematical Society CKMS

Approximate fibrations provide a useful class of maps. Fibrators give instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that rational homology spheres with some additional conditions are codimension-$k$ PL fibrators and PL manifolds with trivial homology groups in some range can be codimension-$k ~(k> 2)$ PL fibrators.

Keywords: approximate fibration, degree of a map, codimension-$k$ fibrator, $m$-fibrator, hopfian manifold, normally cohopfian, sparsely Abelian

MSC numbers: Primary 57N15, 55R65; Secondary 57N25, 54B15