A note on orientation-reversing distance one surgeries on non-null-homologous knots.

We show that there are no distance one surgeries on non-null-homologous knots in M that yield -M (M with opposite orientation) if M is a 3-manifold obtained by a Dehn surgery on a knot K in S^{3}, such that the order of its first homology is divisible by 9 but is not divisible by 27. As an application, we show several knots, including the (2,9) torus knot, do not have chirally cosmetic bandings. This simplifies the proof of a result first proven by Yang that the (2,k) torus knot (k>1) has a chirally cosmetic banding if and only if k=5. [ABSTRACT FROM AUTHOR]