TWISTED BLANCHFIELD PAIRINGS AND TWISTED SIGNATURES II: RELATION TO CASSON-GORDON INVARIANTS

Abstract This paper studies twisted signature invariants and twisted linking forms, with a view toward obstructions to knot concordance. Given a knot K and a representation $\rho $ of the knot group, we define a twisted signature function $\sigma _{K,\rho } \colon S^1 \to \mathbb {Z}$ . This invariant satisfies many of the same algebraic properties as the classical Levine-Tristram signature $\sigma _K$ . When the representation is abelian, $\sigma _{K,\rho }$ recovers $\sigma _K$ , while for appropriate metabelian representations, $\sigma _{K,\rho }$ is closely related to the Casson-Gordon invariants. Additionally, we prove satellite formulas for $\sigma _{K,\rho }$ and for twisted Blanchfield forms.