  The cosmetic crossing conjecture (also known as the "nugatory crossing
conjecture") asserts that the only crossing changes that preserve the oriented
isotopy class of a knot in the 3-sphere are nugatory. We use the Dehn surgery
characterization of the unknot to prove this conjecture for knots in integer
homology spheres whose branched double covers are L-spaces satisfying a
homological condition. This includes as a special case all alternating and
quasi-alternating knots with square-free determinant. As an application, we
prove the cosmetic crossing conjecture holds for all knots with at most nine
crossings and provide new examples of knots, including pretzel knots,
non-arborescent knots and symmetric unions for which the conjecture holds.

Geometric Topology