$L^2$-Burau maps and $L^2$-Alexander torsions

Fathi Ben Aribi; Anthony Conway

$L^2$-Burau maps and $L^2$-Alexander torsions

Geometric Topology 2016-08-03 v1

Authors: Fathi Ben Aribi , Anthony Conway

Abstract

It is well known that the Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define $L^2$ -Burau maps and use them to compute some $L^2$ -Alexander torsions of links. As an application, we prove that the $L^2$ -Burau maps distinguish more braids than the Burau representation.

Keywords

L^2-Burau maps L^2-Alexander torsions braid group Burau representation Alexander polynomial links knot invariants

Cite

@article{arxiv.1608.00752,
  title  = {$L^2$-Burau maps and $L^2$-Alexander torsions},
  author = {Fathi Ben Aribi and Anthony Conway},
  journal= {arXiv preprint arXiv:1608.00752},
  year   = {2016}
}

Comments

17 pages, 4 figures

Related papers

View all related →