Topology Seminar

SPEAKER: Prof. Colin Adams, Williams College

TITLE: Turning Knots into Flowers

ABSTRACT: Knots have traditionally been investigated by considering projections with crossings where two strands of the knot cross one another. Here, we consider multi-crossings (or n-crossings) where n strands of the knot cross at a single point. We show that for each integer n greater than or equal to 2, every knot has a projection made up entirely of n-crossings, and therefore a minimal n-crossing number c_n(K). We

investigate what is known about c_n(K) and then show that for every knot there is an n such that c_n(K) = 1. In fact, every knot has a projection with a single multi-crossing that looks like a daisy. We will consider the implications of this.