Abstract
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.
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