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Chan-Ho Suh

Publications and source records attributed to Chan-Ho Suh.

3 recordsLinked to original sources
arXiv2010

Boundary-twisted normal form and the number of elementary moves to unknot

Suppose $K$ is an unknot lying in the 1-skeleton of a triangulated 3-manifold with $t$ tetrahedra. Hass and Lagarias showed there is an upper bound, depending only on $t$, for the minimal number of elementary moves to untangle $K$. We give a simpler proof, utilizing a normal form for surfaces whose boundary is contained in the 1-skeleton of a triangulated 3-manifold. We also obtain a significantly better upper bound of $2^{120t+14}$ and improve the Hass--Lagarias upper bound on the number of Reidemeister moves needed to unknot to $2^{10^5 n}$, where $n$ is the crossing number.

math.GT↗
arXiv2010

The Unknotting Problem and Normal Surface Q-Theory

Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$ is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory, if $M$ contains an essential surface, then the projective solution space has an essential surface at a vertex. One interesting situation not covered by this theorem is when $M$ is boundary reducible, e.g. $M$ is an unknot complement. We prove that in this case $M$ has an essential disc at a vertex of the Q-projective solution space.

math.GT↗