SU(2)-cyclic surgeries and the pillowcase

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• Steven Sivek, Imperial College
• Wednesday 15 November 2017, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

The cyclic surgery theorem of Culler, Gordon, Luecke, and Shalen 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 weaker 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 “pillowcase”, we will show that if it has infinitely many SU(2)-cyclic surgeries, 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 limit is a boundary slope for the knot. As a corollary, it follows that for any nontrivial knot, the set of SU(2)-cyclic surgery slopes is bounded. This is joint work with Raphael Zentner.

This talk is part of the Differential Geometry and Topology Seminar series.

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