Twisted Blanchfield pairings and decompositions of 3-manifolds

Abstract

We prove a decomposition formula for twisted Blanchfield pairings of 3-manifolds. As an application we show that the twisted Blanchfield pairing of a 3-manifold obtained from a 3-manifold Y with a representation $\phi: Z[\pi_1(Y)] \to R$, infected by a knot J along a curve $\eta$ with $\phi(\eta) \neq 1$, splits orthogonally as the sum of the twisted Blanchfield pairing of Y and the ordinary Blanchfield pairing of the knot J, with the latter tensored up from $Z[t,t^{-1}]$ to R.