On Alexander modules and Blanchfield forms of null-homologous knots in rational homology spheres

Details On Alexander modules and Blanchfield forms of null-homologous knots in rational homology spheres On Alexander modules and Blanchfield forms of null-homologous knots in rational homology spheres

2011-04-23

arxiv.org/abs/1104.4585v1

Journal of Knot Theory and Its Ramifications 21, 5 (2012) 1250042 (21 pages)

Mathematics

Algebraic Topology

Submitted to the Journal of Knots Theory and its Ramifications

Scientific paper

10.1142/S0218216511009947

In this article, we give a classification of Alexander modules of null-homologous knots in rational homology spheres. We characterize these modules A equipped with their Blanchfield forms $\phi$, and the modules A such that there is a unique isomorphism class of $(A,\phi)$, and we prove that for the other modules A, there are infinitely many such classes. We realise all these $(A,\phi)$ by explicit knots in rational homology spheres.

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