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SUMMARY:Louis H Kauffman (University of Illinois at Chicago)
DTSTART:20240111T210000Z
DTEND:20240111T220000Z
DTSTAMP:20260423T022923Z
UID:GEOTOP-A/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/71/
 ">Reconnection Numbers of Knotted Vortices</a>\nby Louis H Kauffman (Unive
 rsity of Illinois at Chicago) as part of GEOTOP-A seminar\n\n\nAbstract\nK
 notted vortices such as those produced in water by Kleckner and Irvine ten
 d to transform by reconnection to collections of unknotted and unlinked ci
 rcles. The reconnection number $R(K)$ of an oriented knot of link $K$ is t
 he least number of reconnections (oriented re-smoothings) needed to unknot
 /unlink $K$. Putting this problem into the context of knot cobordism\, we 
 show\, using Rasmussen's Invariant that the reconnection number of a posit
 ive knot is equal to twice the genus of its Seifert spanning surface. In p
 articular an (a\,b) torus knot has $R=(a−1)(b−1)$. For an arbitrary un
 splittable positive knot or link $K$\, $R(K)=c(K)−s(K)+1$ where $c(K)$ i
 s the number of crossings of K and $s(K)$ is the number of Seifert circles
  of $K$. Examples of vortex dynamics are illustrated in the talk.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/71/
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