The index and nullity of the Lawson surfaces ξg,1

We prove that the Lawson surface ξg,1 in Lawson’s original notation, which has genus g and can be viewed as a desingularization of two orthogonal great two-spheres in the round three-sphere S3, has index 2g+3 and nullity 6 for any genus g≥2. In particular ξg,1 has no exceptional Jacobi fields, which means that it cannot “flap its wings” at the linearized level and is C1-isolated.