arXiv subjects

Hajer Jebali

Publications and source records attributed to Hajer Jebali.

4 recordsLinked to original sources

arXiv2021

On a class of Hausdorff measure of cartesian product sets

In this paper, we study, in a separable metric space, a class of Hausdorff measures $\mathcal{H}_\mu^{q, \xi}$ defined using a measure $\mu$ and a premeasure $\xi$. We discuss a Hausdorff structure of product sets. Weighted Hausdorff measures $\mathcal{W}_\mu^{q, \xi}$ appeared as an important tool when studying the product sets. When $\mu$ and $\xi$ are blanketed, we prove that $\mathcal{H}_\mu^{q, \xi} = \mathcal{W}_\mu^{q, \xi}$. As an application, the case when $\xi$ is defined as the Hausdorff function is considered.

math.CA↗

arXiv2017

Extended periodic links and HOMFLYPT polynomial

Extended strongly periodic links have been introduced by Przytycki and Sokolov as a symmetric surgery presentation of three-manifolds on which the finite cyclic group acts without fixed points. The purpose of this paper is to prove that the symmetry of these links is reflected by the first coefficients of the HOMFLYPT polynomial.

math.GT↗

arXiv2008

Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$

Let K be a knot in $S^3$ and $X$ its complement. We study deformations of reducible metabelian representations of the knot group $π_1(X)$ into $SL(3,\mathbb{C})$ which are associated to a double root of the Alexander polynomial. We prove that these reducible metabelian representations are smooth points of the representation variety and that they have irreducible non metabelian deformations.

math.GT↗

arXiv2008

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.

math.GT↗