**Alexander Representation of Tangles **

* Stephen Bigelow, Alessia Cattabriga, Vincent Florens *

**Abstract**

A tangle is an oriented 1-submanifold of the cylinder whose endpoints lie on the two disks in the boundary of the cylinder. Using an algebraic tool developed by Lescop, we extend the Burau representation of braids to a functor from the category of oriented tangles to the category of