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CATEGORIES:Topology Seminar
SUMMARY:Links with splitting number one - Marc Lackenby (O
xford)
DTSTART;TZID=Europe/London:20120508T150000
DTEND;TZID=Europe/London:20120508T160000
UID:TALK36853AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36853
DESCRIPTION:The unknotting number of a knot is an incredibly d
ifficult invariant to compute. In fact\, there are
many knots which are conjectured to have unknotti
ng number 2\nbut for which no proof of this is cur
rently available. It therefore remains an unsolved
problem to find an\nalgorithm that determines whe
ther 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 has\nsplitting numb
er one if some crossing change turns it into a spl
it link. 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 m
ake a hypothesis on their linking number.) The pro
of that the algorithm works uses sutured manifolds
and normal surfaces.
LOCATION:MR9
CONTACT:Dr Andras Juhasz
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