Structure in the band-Gordian graph

Wednesday, June 26, 2019 - 10:30am - 11:30am
Keller 3-180
Allison Moore (University of California, Davis)
Band surgery is a local operation that transforms a knot into another knot or link, with relevance in both low-dimensional topology and the study of reconnection events in DNA. The band-Gordian graph is an abstract graph whose vertices are the isotopy classes of knots. An edge relates a pair of vertices whenever the knots are related by a band surgery. We will prove some topological obstructions to the existence of band surgeries and mention some recent results on the structure of the band-Gordian graph.