• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.173-179
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• 1996

M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere $S^{n＋2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.1-9
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• 2006

M. Reni has shown that there are at most nine mutually inequivalent knots in the 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. By observing that the Z-homology sphere version of M. Reni's result still holds, M. Mecchia and B. Zimmermann showed that there are exactly nine mutually inequivalent, knots in Z-homology 3-spheres whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds, and conjectured that there exist exactly nine mutually inequivalent, knots in the true 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. Their proof used an argument of AID imitations published in 1992. The main result of this paper is to solve their conjecture affirmatively by combining their argument with a theory of strongly AID imitations published in 1997.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.815-834
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• 2012

In this paper, we characterize surgery presentations for $\mathbb{Z}$-homology 3-spheres and $\mathbb{Z}/2\mathbb{Z}$-homology 3-spheres obtained from $S^3$ by Dehn surgery along a knot or link which admits an even net diagram and show that the Casson invariant for $\mathbb{Z}$-homology spheres and the ${\mu}$-invariant for $\mathbb{Z}/2\mathbb{Z}$-homology spheres can be directly read from the net diagram. We also construct oriented 4-manifolds bounding such homology spheres and find their some properties.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.699-709
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• 2008

We study homology of the gauge group associated with the principal $G_2$ bundle over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the aid of homology and cohomology operations.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.779-784
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• 2024

Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.831-837
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• 2020

Let M be the exterior of a hyperbolic link K ∪ L in a homology 3-sphere Y, such that the linking number lk(K, L) is non-zero. In this note we prove that if γ is a slope in ∂N(L) such that the manifold ML(γ) obtained by γ-Dehn filling along ∂N(L) contains a Klein bottle, then there is a bound on Δ(μ, γ), depending on the genus of K and on lk(K, L).