• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.99-109
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• 2006

Approximate fibrations form a useful class of maps. By definition fibrators provide instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that every closed s-hopfian t-aspherical manifold N with sparsely Abelian, hopfian fundamental group and X(N) $\neq$ 0 is a codimension-(t + 1) PL fibrator.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.327-339
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• 2007

Approximate fibrations form a useful class of maps. By definition fibrators provide instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that every closed s-hopfian t-aspherical manifold N with some algebraic conditions and X(N) $\neq$ 0 is a codimension-(2t + 2) PL fibrator.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.491-501
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• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.283-289
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• 2010

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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.79-90
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• 1999

In this paper, we show that any product of a closed orientable n-manifold $N_1$ with finite fundamental group and a closed orientable asgerical m-mainfold $N_2$ with hopfian fundamental group, where X($N_1$) and X($N_2$) are nonzero, is a condimension 2 fibrator. Moreover, if <$\pi_i(N_1)$=0 for 1$N_1\timesN_2$ is a codimension k PL fibrator.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.841-846
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• 2006

Suppose that F is a closed t-aspherical PL n-manifold with finite, sparsely abelian ${\pi}_1(F)$ and A is a closed aspherical PL m-manifold with hopfian, normally cohopfian ${\pi}_1(A)$. If $X(F){\neq}0{\neq}X(A)$, then $F{\times}A$ is a codimension-(t+1) PL fibrator.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1077-1085
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• 1996

This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.289-295
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• 2007

We describe some conditions under which the product of two groups with certain property is a group with the same property, and we describe some conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, we find some PL fibrators among the product of fibrators.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.337-343
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• 2004

Fibrators are closed manifolds which afford instant recognition of approximate fibrations. In this note we determine which 4-manifolds with geometric structure are fibrators.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.641-650
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• 1996

Let G denote an upper semicontinuous(usc) decomposition of an (n + k)-manifold M into closed, connected n-manifolds. What can be said about the decomposition space B = M/G\ulcorner What regularity properties are possessed by the decomposition map $p : M \to B \ulcorner$ Certain forms of these questions have been addressed by D. Coram and pp. Duvall [C-D].