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SUMMARY:Mehdi Yazdi (Oxford)
DTSTART:20201008T140000Z
DTEND:20201008T143000Z
DTSTAMP:20260423T003234Z
UID:GaTO/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/28/">Th
 e complexity of determining knot genus in a fixed three-manifold</a>\nby M
 ehdi Yazdi (Oxford) as part of Geometry and topology online\n\n\nAbstract\
 n<p>\n        The <i>genus</i> of a knot in a three-manifold is\n        d
 efined to be the minimum genus of a compact\, orientable\n        surface 
 bounding that knot\, if such a surface exists.  In\n        particular a k
 not can be untangled if and only if it has genus\n        zero.  We consid
 er the computational complexity of determining\n        knot genus.  Such 
 problems have been studied by several\n        mathematicians\; among them
  are the works of\n        Hass-Lagarias-Pippenger\, Agol-Hass-Thurston\, 
 Agol and\n        Lackenby.  For a fixed three-manifold the knot genus pro
 blem asks\,\n        given a knot \\(K\\) and an integer \\(g\\)\, whether
  the genus of \\(K\\) is\n        equal to \\(g\\).  Marc Lackenby proved 
 that the knot genus problem\n        for the three-sphere lies in NP.  In 
 joint work with Lackenby\, we\n        prove that this can be generalised 
 to any fixed\, compact\,\n        orientable three-manifold\, answering a 
 question of\n        Agol-Hass-Thurston from 2002.\n      </p>\n
LOCATION:https://researchseminars.org/talk/GaTO/28/
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