Journal of the
Korean Mathematical Society JKMS

In topological category, we show that a bundle
structure $N=F_1\tilde{\times}F_2$ is a codimension $2$ fibrator, where
$F_i$(i=1,2) is an orientable asherical closed manifold with $\chi(F_i)\ne 0$
and its fundamental group is hophian. Also, we show that a Hophian n-manifold
$N$ is a codimension $m>2$ fibrator if it is a codimension 2 fibrator,
$\pi_{i}(N)=0$ for $1 proper subgroup isomorphic to $\pi_{1}(N)/A$, with A an Abelian subgroup. As a
result, a product $N=S^{n}\times F$ of any $n$-sphere $S^{n}$ $(n\ge 3)$ and any
orientable closed surface $F$ with $\chi(F)<0$ is a codimension $(n-1)$ PL
fibrator in PL category.

Keywords: Approximate fibration, Codimension $k$ fibrator, Hopfian group, Hyperhopfian group, Hopfian manifold, Aspherical manifold

MSC numbers: 57N15; 55R65