On a Theorem of Burde and de Rham

有限展示pro-$p$群的Burde--de Rham定理研究

On the Burde--de Rham theorem for finitely presented pro-$p$ groups

该研究在关系元总次数为0的假设下探讨有限展示pro-$p$群的Burde--de Rham定理，给出岩泽理论条件下的高维等实例，并研究相关上同调解释。

Irreducible representations of knot groups into SL(n,C)

The aim of this article is to study the existence of certain reducible, metabelian representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$ which generalise the representations studied previously by G.~Burde and G.~de Rham. Under specific hypotheses we prove the existence of irreducible deformations of such representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$.

General perversities and L^2 de Rham and Hodge theorems for stratified pseudomanifolds

Given a compact stratified pseudomanifold with a Thom-Mather stratification and a class of riemannian metrics over its regular part, we study the relationships between the $L^{2}$ de Rham and Hodge cohomology and the intersection cohomology of $X$ associated to some perversities. More precisely, to a kind of metric which we call \emph{quasi edge with weights}, we associate two general perversities in the sense of G. Friedman, $p_{g}$ and its dual $q_{g}$. We then show that the absolute $L^{2}$ Hodge cohomology is isomorphic to the maximal $L^{2}$ de Rham cohomology and this is in turn isomorph…

Module d'Alexander et représentations métabéliennes

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.