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pro vyhledávání: '"Cho, Sangbum"'
The genus-$g$ Goeritz group is the group of isotopy classes of orientation-preserving self-homeomorphisms of the $3$-sphere that preserve the genus-$g$ Heegaard splitting of the $3$-sphere. In 1933, Goeritz found first a finite generating set of the
Externí odkaz:
http://arxiv.org/abs/2406.13309
The Powell Conjecture states that four specific elements suffice to generate the Goeritz group of the Heegaard splitting of the $3$-sphere. We present an alternative proof of the Powell Conjecture when the genus of the splitting is $3$, and suggest a
Externí odkaz:
http://arxiv.org/abs/2402.07438
Autor:
Cho, Sangbum, Lee, Jung Hoon
A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is then defin
Externí odkaz:
http://arxiv.org/abs/2401.02184
Autor:
Cho, Sangbum, Lee, Jung Hoon
Given a Heegaard splitting of the $3$-sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting. It is an open question whether the primitive disk complex is connected or
Externí odkaz:
http://arxiv.org/abs/2208.01852
Any knot $K$ in genus-$1$ $1$-bridge position can be moved by isotopy to lie in a union of $n$ parallel tori tubed by $n-1$ tubes so that $K$ intersects each tube in two spanning arcs, which we call a leveling of the position. The minimal $n$ for whi
Externí odkaz:
http://arxiv.org/abs/1812.11531
Given a genus-$g$ Heegaard splitting of the $3$-sphere with $g \ge 3$, we show that the primitive disk complex for the splitting is not weakly closed under disk surgery operation. That is, there exist two primitive disks in one of the handlebodies of
Externí odkaz:
http://arxiv.org/abs/1812.10241
Autor:
Cho, Sangbum, Koda, Yuya
We give an alternative proof of a result of Kobayashi and Saeki that every genus one $1$-bridge position of a non-trivial $2$-bridge knot is a stabilization.
Comment: 10 pages, 4 figures
Comment: 10 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/1704.03658
Autor:
Cho, Sangbum, Koda, Yuya
The manifold which admits a genus-$2$ reducible Heegaard splitting is one of the $3$-sphere, $\mathbb{S}^2 \times \mathbb{S}^1$, lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the
Externí odkaz:
http://arxiv.org/abs/1702.05306
Autor:
Cho, Sangbum, Koda, Yuya
A manifold which admits a reducible genus-$2$ Heegaard splitting is one of the $3$-sphere, $S^2 \times S^1$, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is the $3$-sphe
Externí odkaz:
http://arxiv.org/abs/1512.06342