Twisted Blanchfield Pairings and Twisted Signatures Ii: Relation to Casson-Gordon Invariants

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 ρ of the knot group, we define a twisted signature function σ K,ρ S¹ → Z . This invariant satisfies many of the same algebraic properties as the classical Levine-Tristram signature σ K . When the representation is abelian, σ K,ρ recovers σ K , while for appropriate metabelian representations, σ K,ρ is closely related to the Casson-Gordon invariants. Additionally, we prove satellite formulas for σ K,ρ and for twisted Blanchfield forms.