Type: Seminar

Distribution: World

Expiry: 16 Apr 2013

Auth: gilesg@como.maths.usyd.edu.au

From the ancient Gordian knot to today’s inexplicably tangled headphone wires, people have wanted to know whether knots are unknottable. Considering for instance a knot tied in a shoelace, a mathematician would argue that any knot-tying process is completely reversible, and is therefore always unknottable. But what if, after tying such a knot, the two ends of the shoelace were fused together, and cutting wasn’t allowed? This is essentially the topological definition of a knot, and the question of whether two arbitrary knots are the same (or indeed unknottable) was a fundamental problem that knot theorists tangled with up until the 20th century. Even today, the only known recognition algorithms are very slow and have unknown complexity. This talk will introduce the concept of topological knots and explore some of the simpler approaches that were taken in attempts to prove the knot recognition problem. The content will be accessible to all audiences, and will work from basic definitions to weak knot invariants to (time permitting) knot polynomials.

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