GTA Seminar: Coward -- Unknotting Genus One Knots

Speaker: Dr. Alexander Coward (Sydney)

Time: Tuesday, Sept. 18, 12(NOON)--1PM

Room: AGR (Carslaw 829)

Lunch: after the talk (at Taste at Sydney Uni, i.e. 
"Law School Annex Cafe")

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Title: Unknotting Genus One Knots

Abstract: an unknotting crossing change on a knot is a way of passing
the knot through itself so that the resulting curve is unknotted. In
general it is very hard to determine whether a given knot admits an
unknotting crossing change. In this talk we address a related
question: Given a knot which admits an unknotting crossing change, how
many different ways are there of unknotting it? We prove that for all
genus one knots an unknotting crossing change is unique, up to a
suitable notion of equivalence, with the exception of the figure-eight
knot which admits exactly two unknotting crossing changes. The proof 
will be presented so as to be understandable to non-experts. This is 
joint work with Marc Lackenby.

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Web site for Geometry Seminar is at: 

http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html