Department of Mathematics

Geometry and Topology

  •  Renaud Detcherry, Bourgogne
  •  A quantum obstruction to purely cosmetic surgeries
  •  03/30/2021
  •  11:00 AM - 11:50 AM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (gaohongh@msu.edu)

The cosmetic surgery conjecture asks whether it is possible that two Dehn-surgeries on the same non-trivial knot in S³ give the same oriented 3-manifolds. We will present new obstructions for a knot to admit purely cosmetic surgeries, using Reshetikhin-Turaev invariants. In particular, we will show that if a knot admits purely cosmetic surgeries, then the slopes of the surgery are +-1/5k unless the Jones polynomial of K is 1 at the fifth root of unity.

 

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Michigan State University
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