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

Abstract

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 for characterizing slopes.

19 pages, many figures

Cited by in corpus (9)

• Purely cosmetic surgeries and pretzel knots
• Two-bridge knots admit no purely cosmetic surgeries
• Characterizing slopes for $5_2$
• 3-braid knots do not admit purely cosmetic surgeries
• Alternating odd pretzel knots and chirally cosmetic surgeries
• Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures
• A note on chirally cosmetic surgery on cable knots
• On constraints for knots to admit chirally cosmetic surgeries and their calculations
• A non-torus positive 2-bridge knot does not admit chirally cosmetic surgeries