Categorified invariants and the braid group
Geometric Topology
2013-07-29 v2 Quantum Algebra
Representation Theory
Abstract
We investigate two "categorified" braid conjugacy class invariants, one coming from Khovanov homology and the other from Heegaard Floer homology. We prove that each yields a solution to the word problem but not the conjugacy problem in the braid group.
Keywords
Cite
@article{arxiv.1212.2222,
title = {Categorified invariants and the braid group},
author = {John A. Baldwin and J. Elisenda Grigsby},
journal= {arXiv preprint arXiv:1212.2222},
year = {2013}
}
Comments
12 pages, 2 figures. Version 2 has a new, entirely combinatorial, proof that sutured annular Khovanov homology detects the trivial braid, involving a relationship between Plamenevskaya's invariant of transverse links and the Dehornoy order on the braid group