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

## TL;DR

This paper uses the LMO invariant to establish new constraints on when knots in S^3 can undergo cosmetic or Lens space surgeries, advancing understanding of knot surgery phenomena.

## Contribution

It introduces novel constraints derived from the LMO invariant for cosmetic and Lens space surgeries on knots in S^3.

## Key findings

- Constraints for cosmetic surgery based on LMO invariant
- Restrictions on knots admitting Lens space surgeries
- Insights into characterizing slopes for knots

## 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.