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Braid Index Bounds Ropelength From Below

Banff International Research Station for Mathematical Innovation and Discovery

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 $O(n)$.

Mathematics; Biology and other natural sciences; Manifolds and cell complexes; Mathematical biology

video/mp4

Author affiliation: University of North Carolina

2019-09-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71725

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/