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Wednesday, March 23, 2016

4:15 PM - 5:30 PM (ET)

Exley Science Center Tower ESC 638

Event Type

Seminar/Colloquium

Contact

Canalia, Caryn

2182

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=66938

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.