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SUMMARY:The complexity of the knot genus problem - Mehdi Yazdi (Oxford)
DTSTART:20181116T134500Z
DTEND:20181116T144500Z
UID:TALK110770@talks.cam.ac.uk
CONTACT:Richard Webb
DESCRIPTION:The genus of a knot in a 3-manifold is defined to be the minim
 um genus of a compact\, orientable surface bounding that knot\, if such a 
 surface exists. We consider the computational complexity of determining kn
 ot genus. Such problems have been studied by several mathematicians\; amon
 g them are the seminal works of Hass--Lagarias--Pippenger\, Agol--Hass--Th
 urston\, 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 t
 o g. Agol and Lackenby have proved that the knot genus problem for the 3-s
 phere lies in NP. In joint work with Marc Lackenby\, we prove that this ca
 n be generalised to any fixed\, closed\, orientable 3-manifold. This answe
 rs a question of Agol--Hass--Thurston.
LOCATION:CMS\, MR13
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