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.
Citation
Fathi Ben Aribi. Anthony Conway. "$L^2$-Burau maps and $L^2$-Alexander torsions." Osaka J. Math. 55 (3) 529 - 545, July 2018.