Commentarii Mathematici Helvetici

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Volume 81, Issue 4, 2006, pp. 755–781
DOI: 10.4171/CMH/72

Published online: 2006-12-31

Higher-order linking forms for knots

Constance Leidy[1]

(1) University of Pennsylvania, Philadelphia, United States

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.

Keywords: Blanchfield form, Alexander module, knot group, derived series, localization of rings

Leidy Constance: Higher-order linking forms for knots. Comment. Math. Helv. 81 (2006), 755-781. doi: 10.4171/CMH/72