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BIRS Workshop Lecture Videos

Braid Index Bounds Ropelength From Below Diao, Yuanan


For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more than one component, different orientations of the components of $K$ may result in different link types and hence different braid indices. We define the largest braid index among all braid indices corresponding to all possible orientation assignments of $K$ the absolute braid index of $K$ and denote it by $\textbf{b}(K)$. In this talk, we show that there exists a constant $a>0$ such that $L(K)\ge a \textbf{b}(K) $ for any $K$, i.e., the ropelength of any link is bounded below by its absolute braid index (up to a constant factor). In particular, the ropelength of the $(2n,2)$ torus link is of the order of $O(n)$.

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