Higher-order linking forms for 3-manifolds

Given a closed, oriented, connected 3-manifold, M, we define higher-order linking forms on the higher-order Alexander modules of M. These higher-order linking forms generalize similar linking forms for knots previously studied by the author, which were themselves generalizations of the classical Blanchfield linking form for a knot. We also investigate the effect of the construction known as “infection by a knot” on these linking forms.