Module d'Alexander et repr\'esentations m\'etab\'eliennes

Abstract

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.