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 $M\times M\to\mathbb{ F}(t)/\mathbb{ F}[t^{ \pm1}]$ for $\mathbb{ F}=\mathbb{ R},\mathbb{ C}$, where $M$ is a torsion $\mathbb{ F}[t^{ \pm 1}]$-module. Along the way, we classify such linking forms up to isometry and Witt equivalence and study whether they can be represented by matrices.
Categories: math.GT