Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
The computational complexity of knot genus in a fixed 3manifold
Speaker:
Mehdi Yazdi, University of Oxford
Date, Time, and Venue: Wednesday, January 1  11:0011:45  Hall 2
Abstract:
The genus of a knot in a 3manifold is defined to be the minimum genus of a compact, orientable surface bounding that knot, if such a surface exists. In particular a knot can be untangled if and only if it has genus zero. We consider the computational complexity of determining knot genus. Such problems have been studied by several mathematicians; among them are the seminal works of HassLagariasPippenger, AgolHassThurston, Agol and Lackenby. For a fixed 3manifold the knot genus problem asks, given a knot K and an integer g, whether the genus of K is equal to g. Marc Lackenby proved that the knot genus problem for the 3sphere lies in NP. In joint work with Lackenby, we prove that this can be generalised to any fixed, compact, orientable 3manifold, answering a question of AgolHassThurston from 2002.
