Categorified invariants and the braid group
arXiv:1212.2222
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.
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