Geunyoung Kim

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math.GT2026

Bridge position of 3-manifolds embedded in the 5-sphere

Román Aranda, Sarah Blackwell, Geunyoung Kim +2

We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and t…

math.GT2023

Pants distances of knotted surfaces in 4-manifolds

Román Aranda, Sarah Blackwell, Devashi Gulati +4

We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine t…

math.GT2023

$n$ -knots in $S^{n} \times S^{2}$ and contractible $(n + 3)$ -manifolds

Geunyoung Kim

In $1961$ , Mazur constructed a contractible, compact, smooth $4$ -manifold with boundary which is not homeomorphic to the standard $4$ -ball, using a $0$ -handle, a $1$ -handle and a $…

Bridge position of 3-manifolds embedded in the 5-sphere

Pants distances of knotted surfaces in 4-manifolds

n-knots in Sn×S2 and contractible (n+3)-manifolds

$n$ -knots in $S^{n} \times S^{2}$ and contractible $(n + 3)$ -manifolds