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SUMMARY:Marc Lackenby (University of Oxford)
DTSTART:20200721T140000Z
DTEND:20200721T151500Z
DTSTAMP:20260423T005836Z
UID:rlgts/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/rlgts/11/">K
 not genus in a fixed 3-manifold</a>\nby Marc Lackenby (University of Oxfor
 d) as part of Regensburg low-dimensional geometry and topology seminar\n\n
 \nAbstract\nThe genus of a knot is the minimal genus of any of its Seifert
  surfaces. This is a fundamental measure of a knot's complexity. It genera
 lises naturally to homologically trivial knots in an arbitrary 3-manifold.
  Agol\, Hass and Thurston showed that the problem of determining the genus
  of a knot in a 3-manifold is hard. More specifically\, the problem of sho
 wing that the genus is at most some integer g is NP-complete. Hence\, the 
 problem of showing that the genus is exactly some integer g is not in NP\,
  assuming a standard conjecture in complexity theory. On the other hand\, 
 I proved that the problem of determining the genus of a knot in the 3-sphe
 re is in NP. In my talk\, I will discuss the problem of determining knot g
 enus in a fixed 3-manifold. I will outline why this problem is also in NP\
 , which is joint work with Mehdi Yazdi. The proof involves the computation
  of the Thurston norm ball for knot exteriors.\n
LOCATION:https://researchseminars.org/talk/rlgts/11/
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