The eta-invariant torsion conjecture for boundary links

Let $q>1$ and let $(L,\varphi)$ be an $F_m$-link concordance class in $C_{2q+1}(F_m)$. For each positive integer $k$, let $R_k(F_m)$ denote the space of $k$-dimensional unitary representations of the free group $F_m$, and let $\rho(M_L,\varphi)(\alpha)$ be the associated rho-invariant. Eta-invariant torsion conjecture. If, for all $k$, $\rho(M_L,\varphi)(\alpha)=0$ on a dense subset of representations $\alpha\in R_k(F_m)$, then $(L,\varphi)$ represents a torsion element. The conjecture proposes that vanishing of these rho-invariants for dense sets of representations detects torsion in the boundary-link concordance group; its resolution is not specified in the source.