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SUMMARY:Links with splitting number one - Marc Lackenby (Oxford)
DTSTART:20120508T140000Z
DTEND:20120508T150000Z
UID:TALK36853@talks.cam.ac.uk
CONTACT:Dr Andras Juhasz
DESCRIPTION:The unknotting number of a knot is an incredibly difficult inv
 ariant to compute. In fact\, there are many knots which are conjectured to
  have unknotting number 2\nbut for which no proof of this is currently ava
 ilable. It therefore remains an unsolved problem to find an\nalgorithm tha
 t determines whether a knot has unknotting number one. In my talk\, I will
  show that an analogous problem for links is soluble. We say that a link h
 as\nsplitting number one if some crossing change turns it into a split lin
 k. I will give an algorithm that\ndetermines whether a link has splitting 
 number one. (In the case where the link has two components\, we must make 
 a hypothesis on their linking number.) The proof that the algorithm works 
 uses sutured manifolds and normal surfaces.
LOCATION:MR9
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