arXiv subjects

Hee Jung Kim

Publications and source records attributed to Hee Jung Kim.

21 records · Page 2Linked to original sources

arXiv2009

Modifying surfaces in 4-manifolds by twist spinning

In this paper, given a knot K, for any integer m we construct a new surface Sigma_K(m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the `rim surgery' which was introduced by Fintushel and Stern, by doing additional twist spinning. We investigate the diffeomorphism type and the homeomorphism type of (X,Sigma) after the surgery. One of the main results is that for certain pairs (X,Sigma), the smooth type of Sigma_K(m) can be easily distinguished by the Alexander polynomial of the knot K and the homeomorphism type depends on the number of twist and the knot. In particular, we get new examples of knotted surfaces in CP^2, not isotopic to complex curves, but which are topologically unknotted.

math.GT↗

arXiv2008

Topological triviality of smoothly knotted surfaces in 4-manifolds

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we construct examples of knotted surfaces whose complements have cyclic fundamental groups.

math.GT↗

arXiv2008

Smooth surfaces with non-simply-connected complements

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth s-cobordism and hence are topologically equivalent for good groups.

math.GT↗