Alternating knots with unknotting number one

Duncan McCoy (University of Glasgow)

Monday 20th January, 2014 16:00-17:00 Maths 204

Abstract

It is conjectured that any knot with unknotting number one must have an unknotting crossing in a minimal diagram. Whilst still unresolved in general, this conjecture is now known to be true for alternating knots. The proof builds on the work of Greene, who showed that if an alternating knot has unknotting number one, then the Goeritz form corresponding to any alternating diagram must obey so-called 'change-maker' conditions. I will explain the change-maker conditions and indicate how they can be used to identify unknotting crossings in alternating diagrams.

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