Knots, graphs, and the Alexander polynomial

Knots, graphs, and the Alexander polynomial

Thu, 25/02/2010
12:00 		Jessica Banks (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Knots, graphs, and the Alexander polynomial
In 2008, Juhasz published the following result, which was proved using sutured Floer homology. Let $ K $ be a prime, alternating knot. Let $ a $ be the leading coefficient of the Alexander polynomial of $ K $. If $ |a|<4 $, then $ K $ has a unique minimal genus Seifert surface. We present a new, more direct, proof of this result that works by counting trees in digraphs with certain properties. We also give a finiteness result for these digraphs.