Recognising the unknot

Recognising the unknot

-
Marc Lackenby, University of Oxford

Online Talk 

*Please note the time change*

One of the most basic problems in low-dimensional topology is to determine whether a given simple closed curve in 3-space is the unknot. This is known as the "unknotting problem". An algorithm to solve it was given by Wolfgang Haken in the 1960s. However, it remains a significant unresolved question whether there is an algorithm that runs in polynomial time (as a function of the number of crossings in a given knot diagram). In my talk, I will discuss what is known about this question. I will explain why the unknotting problem is known to lie in NP and co-NP, and I will outline a new unknot recognition algorithm that runs in quasi-polynomial time.