Unknot recognition in quasi-polynomial time

Unknot recognition in quasi-polynomial time

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Marc Lackenby, University of Oxford

*Please note the change in time*

Zoom link:https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09


I will outline a new algorithm for unknot recognition that runs in quasi-polynomial time. The input is a diagram of a knot with n crossings, and the running time is 2^{O((log n)^3)}. The algorithm uses hierarchies, normal surfaces and Heegaard splittings.