• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.131-138
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• 2021

In this paper, we define a concept of weak T-fibration which is a generalization of weak H-fibration, and study some properties of weak T-fibration and relations between the weak T-fibration and the Postnikov system for a fibration.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.835-840
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• 2021

In this paper, we compute the rational evaluation subgroup of the Hopf fibration S²ⁿ⁺¹ ↪ ℂP(n). We show that, for the Sullivan model 𝜙 : A → B, where A and B are the minimal Sullivan models of ℂP(n) and S²ⁿ⁺¹ respectively, the evaluation subgroup G_n(A, B; 𝜙) and the relative evaluation subgroup G^rel_n (A, B; 𝜙) of 𝜙 are generated by single elements.

• The Journal of Natural Sciences
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• v.10 no.1
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• pp.9-12
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• 1998

In this paper, we obtain that if $\psi : E \to F$ is a fibrewise fibration then postcomposition $\psi :C_B(Y, E) \to C_B(Y, F)$ is fibrewise fibration and if (X, A) is a closed fibrewise cofibration the the precomposition $\upsilon :C_B(X, E) \to C_B(A, E)$ is also a fibrewise fibration.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.155-158
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• 2004

We give a certain uniqueness properties for the fiber of the Hopf fibration on lens spaces.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.25-33
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• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.505-521
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• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.1-6
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• 2001

We investigate the relationships between the Gottlieb groups and the generalized Gottlieb groups, and study some properties of the generalized Gottlieb groups. Lee and Woo [5] proved that $G_n(X,i_1,X{\times}Y){\simeq_-}G_n(X){\oplus}{\pi}_n(Y)$. We can easily re-prove the above main theorem of [5] using some properties of the generalized Gottlieb groups, and obtain a more powerful result as follows; if $F{\rightarrow}^iE{\rightarrow}^pB$ is a homotopically trivial fibration, then $G_n(F,i,E){\simeq_-}{\pi}_n(B){\oplus}G_n(F)$.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.603-614
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• 2013

In the article we show that nondieomorphic symplectic 4-manifolds which admit marked Lefschetz fibrations can share the same monodromy group. Explicitly we prove that, for each integer g > 0, every knot surgery 4-manifold in a family {$E(2)_K{\mid}K$ is a bered 2-bridge knot of genus g in $S^3$} admits a marked Lefschetz fibration structure which has the same monodromy group.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.445-449
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• 2021

We define the relative self-closeness number N��(g) of a map g : X → Y, which is a generalization of the self-closeness number N��(X) of a connected CW complex X defined by Choi and Lee [1]. Then we compare N��(p) with N��(X) for a fibration $X{\rightarrow}E{\rightarrow\limits^p}Y$. Furthermore we obtain its rationalized result.

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