A Burau–Alexander 2-functor on tangles
Volume 240 / 2018
Fundamenta Mathematicae 240 (2018), 51-79
MSC: Primary 57M25; Secondary 18D05.
DOI: 10.4064/fm274-11-2016
Published online: 4 May 2017
Abstract
We construct a weak $2$-functor from the bicategory of oriented tangles to a bicategory of Lagrangian cospans. This functor simultaneously extends the Burau representation of the braid groups, its generalization to tangles due to Turaev and the first-named author, and the Alexander module of $1$- and $2$-dimensional links.
