"Non UBC"@en .
"DSpace"@en .
"Yuanan Diao"@en .
"2019-09-23T09:17:00Z"@en .
"2019-03-26T14:06"@en .
"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 $O(n)$."@en .
"https://circle.library.ubc.ca/rest/handle/2429/71725?expand=metadata"@en .
"31.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of North Carolina"@en .
"Banff (Alta.)"@en .
"10.14288/1.0380942"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Biology and other natural sciences"@en .
"Manifolds and cell complexes"@en .
"Mathematical biology"@en .
"Braid Index Bounds Ropelength From Below"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/71725"@en .