• 대한수학회보
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• 제26권2호
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• pp.109-114
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• 1989

This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.

• 대한수학회지
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• 제35권2호
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• 대한수학회논문집
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• 제11권2호
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• pp.445-455
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• 1996

In this paper we study the Reidemeister number $R(f_G)$ for a self-map $f_G : (X, G) \to (X, G)$ of the transformation group (X,G), as an extenstion of the Reidemeister number R(f) for a self-map $f : X \to X$ of a topological space X.

• 대한수학회논문집
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• 제11권3호
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• pp.807-814
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• 1996

Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

• 호남수학학술지
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• 제26권4호
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• pp.411-421
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• 2004

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.

• 호남수학학술지
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• 제36권2호
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• pp.435-454
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• 2014

We show that for any graph G, the proper part of the intersection poset of the corresponding graphical arrangement $\mathcal{A}_G$ has the homotopy type of a wedge of spheres. Furthermore, we also indicate the number of spheres in the wedge, based on the number of spanning forests of G and other graphs that are obtained from G.

• 호남수학학술지
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• 제36권1호
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• pp.85-102
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• 2014

We show that if a graph G is compressed, then the proper part of the intersection poset of the corresponding graphical arrangement $A_G$ has the homotopy type of a wedge of spheres. Furthermore, we also indicate the number of spheres in the wedge, based on the number of adjacent edges of vertices in G.

• Korean Journal of Mathematics
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• 제7권1호
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• pp.131-138
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• 1999

We introduce an extended Jiang subgroup $J(f,x_0,G)$ of the fundamental group of a transformation group as a generalization of the Jiang subgroup $J(f,x_0)$ and show some properties of this extended Jiang subgroup.

• 대한수학회보
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• 제33권2호
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• pp.303-310
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• 1996

The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.

• 대한수학회지
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• 제32권2호
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• pp.171-181
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• 1995

Nielsen coincidence theory is concerned with the estimation of a lower bound for the number of coincidences of two maps $f,g: X \longrightarrow Y$. For this purpose the so-called Nielsen number N(f,g) is introduced, which is a lower bound for the number of coincidences ([1]). The relative Nielsen number N(f : X,A) in the fixed point theory is introduced in [3], which is a lower bound for the number of fixed points for all maps in the relative homotopy class of f:(X,A) $\longrightarrow$ (X,A), and its estimation is given in [5].