Welcome to Geometry and Topology Lab located at Sungshin Women’s University, Seoul, South Korea. Our lab is focused on a classification problem of smooth and symplectic 4-manifolds.
Department of Mathematics
Sungshin Women’s University
2 Bomun-ro 34 Da-gil, Seongbuk-gu
Seoul 02844, Republic of Korea
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Topology and its Applications 153 (2006), pp. 1994-2012
In this article we show that the signature of a Lefschetz fibration coming from a special involution as a product of right handed Dehn twists depends only on the number of genus on the involution axis. We investigate the geography of such Lefschetz fibrations and we identify it with a blow up of a ruled surface. We also get a geography of the Lefschetz fibration coming from a finite order element of mapping class group as a composition of two special involutions.
Journal of the knot theory and its ramifications Vol. 16, No. 4 (2007) pp. 499-521
In the article we study the multi-variable Alexander polynomial of a link in a plat form or in a closed braid form. By using the method, we find an algorithm how to compute the multi-variable Alexander polynomial of the 2a-fold dihedral cover and the a-fold irregular cover of a two bridge knot K(a,b)
Communications in contemporary Mathematics, Vol. 9, No. 5 (2007) pp. 681-690 (Joint work with Jongil Park)
We present a simple way to construct an infinite family of simply connected, nonspin, smooth 4-manifolds with one basic class which do not admit a symplectic structure with either orientation.
Transactions of the AMS Vol. 360 No.11(2008)pp. 5853-5868
In the article, we study the Fintushel-Stern’s knot surgery four manifold E(n)K and their monodromy factorization. For fibered knots we provide a smooth classification of knot surgery 4-manifolds up to twisted fiber sum. We then show that other constructions of 4-manifolds with the same Seiberg-Witten invariants are in fact diffeomorphic.
Mathematische Annalen Vol. 345(2009) pp. 581-597 (Joint work with Jongil Park)
In this article we construct an infinite family of simply connected minimal symplectic 4-manifolds, each of which admits at least two nonisomorphic Lefschetz fibration structures with the same generic fiber. We obtain such examples by performing knot surgery on an elliptic surface E(n) using a special type of 2-bridge knots.
Bulletin of the Korean Mathematical Society Vol.47(2010) No.5 pp. 961-971 (Joint work with Jongil Park)
As an application of ‘reverse engineering’ technique introduced by R. Fintushel, D. Park and R. Stern, we present a simple way to construct an infinite family of exotic ’s for all ,.
Michigan Mathematical Journal Vol. 60(2011) pp. 525-544 (Joint work with Jongil Park)
In this article we study Lefschetz fibration structures on knot surgery 4-manifolds obtained from an elliptic surface E(2) using Kanenobu knots K. As a result, we get an infinite family of simply connected mutually diffeomorphic 4-manifolds coming from a pair of inequivalent Kanenobu knots. We also obtain an infinite family of simply connected symplectic 4-manifolds, each of which admits more than one inequivalent Lefschetz fibration structures of the same generic fiber.
Journal of Symplectic Geometry 13(2015) No.2 pp. 279–303 (Joint work with Jongil Park)
In this article, we show that, at least for non-simply connected case, there exist an infinite family of nondiffeomorphic symplectic 4-manifolds with the same Seiberg-Witten invariants. The main techniques are knot surgery and a covering method developed in Fintushel and Stern’s paper.
Kyungpook Mathematical Journal, Vol. 53 No. 4(2013), pp. 603 –614
In the article we show that nondiffeomorphic 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 admits a marked Lefschetz fibration structure which has the same monodromy group.
arXiv:1503.06272 (Joint work with Jongil Park), Michigan Mathematical Journal(published online)
In this article we construct a family of knot surgery 4-manifolds admitting arbitrarily many nonisomorphic Lefschetz fibration structures with the same genus fiber. We obtain such families by performing knot surgery on an elliptic surface using connected sums of fibered knots obtained by Stallings twist from a slice knot . By comparing their monodromy groups induced from the corresponding monodromy factorizations, we show that they admit mutually nonisomorphic Lefschetz fibration structures.
Proc. Amer. Math. Soc. 145 (2017), pp. 3607-3616.(Joint work with András I. Stipsicz)
We show that the minimal number of singular fibers in a genus- Lefschetz fibration over the torus is at least . As an application, we show that for , for and .
Joint work with Heesang Park, Jongil Park, Dongsoo Shin, Communications of the KMS (published online)
We construct various examples of simply connected minimal complex surfaces of general type with and using -Gorenstein smoothing method.
arXiv:1704.02181(joint work with Hakho Choi and Jongil Park)
In this article we show that all knot surgery 4-manifolds are mutually diffeomorphic after a connected sum with . Hence, by combining a known fact that every simply connected elliptic surface is almost completely decomposable, we conclude that every knot surgery -manifold is also almost completely decomposable.