TWISTED BLANCHFIELD PAIRINGS AND SYMMETRIC CHAIN COMPLEXES

We define the twisted Blanchfield pairing of a symmetric triad of chain complexes over a group ring Z[pi], together with a unitary representation of pi over an Ore domain with involution. We prove that the pairing is sesquilinear, and we prove that it is hermitian and non-singular under certain extra conditions. A twisted Blanchfield pairing is then associated to a 3-manifold together with a decomposition of its boundary into two pieces, and a unitary representation of its fundamental group.