Topology Seminar

Wednesday, March 23, 2016
4:15 PM - 5:30 PM (ET)
Exley Science Center Tower ESC 638
Event Type
Canalia, Caryn

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.

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