Contact cosmetic surgery

Tanushree Shah (Chennai Mathematics Institute)

Abstract: Surgery is a universal operation to go between 3-manifolds. The redundancy in this operation is called cosmetic. Studying this redundancy has been part of Kirby's problem list (1.81A). We added an extra structure to our 3 manifolds, namely, a contact structure, and asked about redundancy for contact manifold surgery. We demonstrate that contact cosmetic surgery is not possible for all knots except for knots 'like' the unknot (for non-slice knots). We also discuss the contact cosmetic surgeries on knots like unknot and make surprising observations.