Communications in Analysis and Geometry

Volume 28 (2020)

Number 2

On LMO invariant constraints for cosmetic surgery and other surgery problems for knots in $S^3$

Pages: 321 – 349



Tetsuya Ito (Department of Mathematics, Kyoto University, Kyoto, Japan)


We use the LMO invariant to find constraints for a knot to admit a purely or reflectively cosmetic surgery. We also get a constraint for knots to admit a lens space surgery, and some information about characterizing slopes.

Received 24 April 2017

Accepted 10 December 2017

Published 6 May 2020