92 citations · 351 across the 18 of their papers we have counts for
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Generalized Heegaard splittings and the disk complex
Jungsoo Kim
Let be an orientable, irreducible -manifold and a weakly reducible, unstabilized Heegaard splitting of of genus at least three. In this art…
On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three III - Generalized Heegaard splittings and mapping classes
Jungsoo Kim
Let be an orientable, irreducible -manifold admitting a weakly reducible genus three Heegaard splitting as a minimal genus Heegaard splitting. In this article, we prove that…
On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem
Jungsoo Kim
Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of the disk complex D(F) consisting…
On unstabilzed genus three critical Heegaard surfaces
Jungsoo Kim
Let be a compact orientable irreducible 3-manifold and be an unstabilized genus three Heegaard splitting of . In this article, we will define a simplicial complex of wea…
Rectangle condition for compression body and 2-fold branched covering
Jungsoo Kim, Jung Hoon Lee
We give the rectangle condition for strong irreducibility of Heegaard splittings of -manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a $2…
A note on the nearly additivity of knot width
Jungsoo Kim
Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k…