边界扭曲的normal form和解开纽结的基本移动次数
Boundary-twisted normal form and the number of elementary moves to unknot
摘要：
设$K$是一个位于具有$t$四面体的三角剖分3-流形的1-骨架上的非纽结. Hass和Lagarias证明了解$K$的最小基本移动数存在一个上界，仅取决于$t$。我们给出了一个更简单的证明，利用一个正常的形式的表面，其边界包含在1骨架的三角形3流形。我们还得到了一个显着更好的上界$2^{120t+14}$和改进的Hass-Lagarias上限的Reidemeister移动的数量需要解开$2^{10^5 n}$，其中$n$是交叉数。
英文摘要：
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.
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