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Computing the braid index using only a knot diagram and knots where the braid index equals the bridge index

Banff International Research Station for Mathematical Innovation and Discovery

We talk about how to read the braid index of certain families of alternating knots from a minimal knot diagram. In addition we talk about a class of knots where the braid index equals the bridge index. These knots seem to have particular physical properties as demonstrated by several experiments. They undergo a periodic motion when sedimenting in a viscous fluid as knotted deformable closed chains, they also seem to achieve a circular minimum as elastic knots when their bending energy (curvature) is minimized.

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

video/mp4

Author affiliation: Western Kentucky University

2019-09-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71772

Unreviewed

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