tag:peatix.com,2011:1 2019-11-02T01:00:39-04:00 Peatix On campus at Wes tag:peatix.com,2016:event-154371 2016-03-23T16:15:00EST 2016-03-23T16:15:00EST

Scott Taylor, Colby College:  Neighbors of knots in the Gordian graph Abstract: Switching a crossing on a knot diagram is one of the simplest methods forconverting one type of knot into another type of knot. The Gordian graph is the graphwhich keeps track of which knot types can be converted into which other knot types bya single crossing change. Its vertex set is the set of knot types and its edge set consistsof pairs of knots which have a diagram wherein they differ at a single crossing. Bridgenumber is a classical knot invariant which is a measure of the complexity of a knot. It canbe re_ned by another, recently discovered, knot invariant known as \bridge distance". Weshow, using arguments that are almost entirely elementary, that each vertex of the Gordiangraph is adjacent to a vertex having arbitrarily high bridge number and bridge distance.This is joint work with Ryan Blair, Marion Campisi, Jesse Johnson, and Maggy Tomova.