The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ℤ₂-torsion if the corresponding Tait-type graph has a cycle of length at least 3. Computations show that torsion of odd order exists but there is no general theory to support these observations. We conjecture that the existence of torsion is related to the braid index.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-13,
author = {J\'ozef H. Przytycki and Radmila Sazdanovi\'c},
title = {Torsion in Khovanov homology of semi-adequate links},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {277-303},
zbl = {1295.57010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-13}
}
Józef H. Przytycki; Radmila Sazdanović. Torsion in Khovanov homology of semi-adequate links. Fundamenta Mathematicae, Tome 227 (2014) pp. 277-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-13/