Splittings of von Neumann rho-invariants of knots.

We give a sufficient condition under which the vanishing property of Cochran–Orr–Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This extends the results of Levine and the authors on distinguishing knots with coprime Alexander polynomials up to concordance. As an application, we show that the knots constructed by Cochran, Orr and Teichner as the first examples of nonslice knots with vanishing Casson–Gordon invariants are not concordant to any knots of genus one. This gives the first examples of concordance genus two knots with vanishing Casson–Gordon invariants. [ABSTRACT FROM PUBLISHER]