On the symmetry of composite ribbon knots

Abstract

The connected-sum of a knot and its mirror image with orientation reversed is a ribbon knot. Conversely, we show that if K0 and K1 are knots which are minimal with respect to ribbon concordance and the connected sum of K0 and K1 is a ribbon number one knot, then K0 is equivalent to the mirror image of K1 with orientation reversed. We also show that the connected sum of two torus knots is a slice knot, then it is a connected sum of a torus knot and its mirror image.