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SUMMARY:SU(2)-cyclic surgeries and the pillowcase - Steven Sivek\, Imperia
 l College
DTSTART:20171115T160000Z
DTEND:20171115T170000Z
UID:TALK77491@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The cyclic surgery theorem of Culler\, Gordon\, Luecke\, and S
 halen implies that any knot in the 3-sphere other than a torus knot has at
  most two nontrivial cyclic surgeries. In this talk\, we investigate the w
 eaker notion of SU(2)-cyclic surgeries on a knot\, meaning surgeries whose
  fundamental groups only admit SU(2) representations with cyclic image. By
  studying the image of the SU(2) character variety of a knot in the “pil
 lowcase”\, we will show that if it has infinitely many SU(2)-cyclic surg
 eries\, then the corresponding slopes (viewed as a subset of RP^1) have a 
 unique limit point\, which is a finite\, rational number\, and that this l
 imit is a boundary slope for the knot. As a corollary\, it follows that fo
 r any nontrivial knot\, the set of SU(2)-cyclic surgery slopes is bounded.
  This is joint work with Raphael Zentner.
LOCATION:MR13
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