$L^2$-Burau maps and $L^2$-Alexander torsions
  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. 
Fathi Ben Aribi and Anthony Conway
math.GT