Module d'Alexander et représentations métabéliennes

Details Module d'Alexander et représentations métabéliennes Module d'Alexander et représentations métabéliennes

2007-09-14

arxiv.org/abs/0709.2306v2

Ann. Fac. Sci. Toulouse Math. 4 (2008) 17 : 751-764

Mathematics

Geometric Topology

To appear in Annales Math\'ematiques de Toulouse

Scientific paper

It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular $2x2$ matrices. In this work, we propose to generalize this result by considering the representations of the knot group into the group of the invertible upper triangular $nxn$ matrices, $n\geq 2$. This approach will enable us to find the decomposition of the Alexander module with complex coefficients.

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