Twisted Blanchfield pairings and twisted signatures I: Algebraic background.

This is the first paper in a series of three devoted to studying twisted linking forms of knots and three-manifolds. Its function is to provide the algebraic foundations for the next two papers by describing how to define and calculate signature invariants associated to a linking form M × M → F (t) / F [ t ± 1 ] for F = R , C , where M is a torsion F [ t ± 1 ] -module. Along the way, we classify such linking forms up to isometry and Witt equivalence and study whether they can be represented by matrices. [ABSTRACT FROM AUTHOR]