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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:SU(2)-cyclic surgeries and the pillowcase - Steven
Sivek\, Imperial College
DTSTART;TZID=Europe/London:20171115T160000
DTEND;TZID=Europe/London:20171115T170000
UID:TALK77491AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/77491
DESCRIPTION:The cyclic surgery theorem of Culler\, Gordon\, Lu
ecke\, and Shalen implies that any knot in the 3-s
phere other than a torus knot has at most two nont
rivial cyclic surgeries. In this talk\, we investi
gate the weaker notion of SU(2)-cyclic surgeries o
n a knot\, meaning surgeries whose fundamental gro
ups only admit SU(2) representations with cyclic i
mage. By studying the image of the SU(2) character
variety of a knot in the “pillowcase”\, we will s
how that if it has infinitely many SU(2)-cyclic su
rgeries\, then the corresponding slopes (viewed as
a subset of RP^1) have a unique limit point\, whi
ch is a finite\, rational number\, and that this l
imit is a boundary slope for the knot. As a coroll
ary\, it follows that for any nontrivial knot\, th
e set of SU(2)-cyclic surgery slopes is bounded. T
his is joint work with Raphael Zentner.
LOCATION:MR13
CONTACT:Ivan Smith
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