A Burau-Alexander 2-functor on tangles
Geometric Topology
2016-11-29 v2
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.
Cite
@article{arxiv.1606.05166,
title = {A Burau-Alexander 2-functor on tangles},
author = {David Cimasoni and Anthony Conway},
journal= {arXiv preprint arXiv:1606.05166},
year = {2016}
}
Comments
25 pages, 4 figures; several portions of the article rewritten in version 2: our 2-category of Lagrangian cospans is in fact a bicategory, and our 2-functor a weak 2-functor. Final version, to appear in Fundamenta Mathematicae