Event time:
Thursday, September 29, 2005 - 12:30pm to 1:30pm
Location:
431 DL
Speaker:
Elizabeth Denne
Speaker affiliation:
Harvard University
Event description:
It is known that for every knotted curve in space, there is a
line intersecting it in four places, a quadrisecant. Comparing the
order of the four points along the line an the knot we can distinguish
three types of quadrisecants; the alternating ones have the most
relevance for the geometry of a knot. I will show that every
(nontrivial tame) knot has an alternating quadrisecant. This result has
applications to the total curvature, second hull and ropelength of
knots.