• East Asian mathematical journal
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• v.34 no.5
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• pp.587-595
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• 2018

In [9], Lee and Sakuma constructed 2-generator non-Hopfian groups each of which has a specific presentation ${\langle}a,b{\mid}R{\rangle}$ satisfying small cancellation conditions C(4) and T(4). In this paper, we prove the SQ-universality of those non-Hopfian groups.

• 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.

• East Asian mathematical journal
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• v.15 no.1
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• pp.135-146
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• 1999

• 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.

• 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.

• 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.

• 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].

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.145-154
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• 1996

In the study of manifold decompositions, a central theme is to understand the source manifold taking advantage of the informations of a base space and a decomposition. The concepts of both Hurewicz fibrations and cell-like maps have played very important roles for investigating the mutual relations of three objects. But it is somewhat restrictive for a decomposition map to be cell-like because its inverse images must have trivial shapes.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.367-374
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• 2003

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.