Peripheral elements in reduced Alexander modules

Abstract

We discuss meridians and longitudes in reduced Alexander modules of classical and virtual links. When these elements are suitably defined, each link component will have many meridians, but only one longitude. Enhancing the reduced Alexander module by singling out these peripheral elements provides a significantly stronger link invariant. In particular, the enhanced module determines all linking numbers in a link; in contrast, the module alone does not even detect how many linking numbers are $0$.

v1: 19 pages, 9 figures. v2: example corrected. 20 pages, 9 figures. v3: 21 pages, 10 figures. Final prepublication version. Further changes may be made before publication in the Journal of Knot Theory and its Ramifications