We define the twisted Blanchfield pairing of a symmetric triad of chain
complexes over a group ring Z[G], together with a unitary representation of G
over an Ore domain with involution.
We prove that the pairing is sesquilinear, and we prove that it is hermitian
and nonsingular 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.Comment: 26 pages. Version 2: the introduction has been rewritten and a new
application has been added in the final section. To appear in Quarterly
Journal of Mat
