• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.787-795
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• 2001

For the generalized nilpotent spaces, e.g. the locally nilpotent space, the residually locally nilpotent space and the space satisfying the condition ($T^{*}$) or ($T^{**}$), we find the pullback property of them. Furthermore we investigate some fiber properties of the space satisfying the condition ($T^{*}$) or ($T^{**}$), especially locally nilpotent space.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.349-355
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• 2000

In this paper we generalize the Whitehead theorem which says that a homology equivalence implies a homotopy equivalence for nilpotent spaces. We make some theorems on a homotopy equivalence of non-nilpotent spaces, e.g., the solvable space or space satisfying the condition (T**) or space X with $\pi$1(X) Engel, or locally nilpotent space with some properties. Furthermore we find some conditions that the Wall invariant will be trivial.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.117-123
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• 1997

• Honam Mathematical Journal
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• v.20 no.1
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• pp.147-152
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• 1998

In this paper, we shall investigate the admittance of a fixed point free deformation(FPFD) on the locally nilpotent spaces when ${\pi}_1(X)$ is infinite. More precisely, for $X{\in}(S_{{\ast}{LN}})$ with ${\pi}_1(X)$ infinite, we prove the admittance of a FPFD where ${\pi}_1(X)$ has the maximal condition on normal subgroups, or ${\pi}_1(X)$ satisfies either the max-${\infty}$ or min-${\infty}$ for non-nilpotent subgroups where $S_{{\ast}{LN}}$ denotes the category of the locally nilpotent spaces and base point preserving continuous maps.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.