Cosmetic surgery on knots

Abstract

This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1–cusped hyperbolic 3–manifold X with a pair of slopes r1 , r2 such that the Dehn filled manifolds X(r1), X(r2) are oppositely oriented copies of the lens space L(49, 18), and there is no homeomorphism h of X such that h(r1) = h(r2). AMS Classification 57N10; 57M25, 57M50