• 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.

• 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.