• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1139-1148
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• 2015

For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1619-1625
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• 2017

The aim of this short note is to give a simple proof of the non-rationality of the double cover of the three-dimensional projective space branched over a sufficiently general quartic.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.691-701
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• 2006

In this paper, we construct a new exotic smooth 4-manifold X which is homeomorphic, but not diffeomorphic, to ${\mathbb{C}}\mathbb{P}^2{\sharp}13\overline{\mathbb{C}\mathbb{P}}^2$. Moreover the manifold X has vanishing Seiberg-Witten invariants for all $Spin^c$-structures of X and has no symplectic structure.