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