The Effect of Infecting Curves on Knot Concordance

Various obstructions to knot concordance have been found using Casson–Gordon invariants, higher-order Alexander polynomials, as well as von-Neumann ρ-invariants. Examples have been produced using (iterated) doubling operations $K\equiv \mathfrak R(\eta, J)$, and considering these as parametrized by invariants of the base knot J and doubling operator $\mathfrak R$. In this paper, we introduce a new method to obstruct concordance. We show that infinitely many distinct concordance classes may be constructed by varying the infecting curve η in $S^{3}-\mathfrak R$. Distinct concordance classes are found even while fixing the base knot, the doubling operator, and the order of η in the Alexander module.