Topology Seminar: "Neighbors of knots in the Gordian graph"
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 for
converting one type of knot into another type of knot. The Gordian graph is the graph
which keeps track of which knot types can be converted into which other knot types by
a single crossing change. Its vertex set is the set of knot types and its edge set consists
of pairs of knots which have a diagram wherein they differ at a single crossing. Bridge
number is a classical knot invariant which is a measure of the complexity of a knot. It can
be re_ned by another, recently discovered, knot invariant known as \bridge distance". We
show, using arguments that are almost entirely elementary, that each vertex of the Gordian
graph 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.
4:15 PM - 5:30 PM EDT
- Exley Science Center Tower ESC 638
- Venue Address
- 45 Wyllys Avenue, Middletown, CT United States