The complexity of the knot genus problem

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• Mehdi Yazdi (Oxford)
• Friday 16 November 2018, 13:45-14:45
• CMS, MR13.

If you have a question about this talk, please contact Richard Webb.

The genus of a knot in a 3-manifold is defined to be the minimum genus of a compact, orientable surface bounding that knot, if such a surface exists. We consider the computational complexity of determining knot genus. Such problems have been studied by several mathematicians; among them are the seminal works of Hass—Lagarias—Pippenger, Agol—Hass—Thurston, Agol and Lackenby. For a fixed 3-manifold the knot genus problem asks, given a knot K and an integer g, whether the genus of K is equal to g. Agol and Lackenby have proved that the knot genus problem for the 3-sphere lies in NP. In joint work with Marc Lackenby, we prove that this can be generalised to any fixed, closed, orientable 3-manifold. This answers a question of Agol—Hass—Thurston.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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