Khovanov complexes of rational tangles
Geometric Topology
2018-12-13 v2 Quantum Algebra
Abstract
We show that the Khovanov complex of a rational tangle has a very simple representative whose backbone of non-zero morphisms forms a zig-zag. Furthermore, this minimal complex can be computed quickly by an inductive algorithm. (For example, we calculate by hand.) We find that the bigradings of the subobjects in these minimal complexes can be described by matrix actions, which after a change of basis is the reduced Burau representation of .
Cite
@article{arxiv.1701.07525,
title = {Khovanov complexes of rational tangles},
author = {Benjamin Thompson},
journal= {arXiv preprint arXiv:1701.07525},
year = {2018}
}
Comments
20 pages. Removed unnecessary exposition from the first version and updated some diagrams and references