Higher-order linking forms for knots

Abstract

We construct examples of knots that have isomorphic $n$th-order Alexander modules, but non-isomorphic $n$th-order linking forms, showing that the linking forms provide more information than the modules alone. This generalizes work of Trotter [T], who found examples of knots that have isomorphic classical Alexander modules, but non-isomorphic classical Blanchfield linking forms.