Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsion. When the underlying algebra is ℤ[x]/(x²), we determine precisely those graphs whose cohomology contains torsion. For a large class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. Our computation could potentially be used to predict the Khovanov-Rozansky sl(m) homology of knots (in particular (2,n) torus knot). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-5,
author = {Laure Helme-Guizon and J\'ozef H. Przytycki and Yongwu Rong},
title = {Torsion in graph homology},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {139-177},
zbl = {1105.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-5}
}
Laure Helme-Guizon; Józef H. Przytycki; Yongwu Rong. Torsion in graph homology. Fundamenta Mathematicae, Tome 189 (2006) pp. 139-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-5/