Torsion in graph homology

Laure Helme-Guizon, Józef H. Przytycki, and Yongwu Rong. "Torsion in graph homology." Fundamenta Mathematicae 190.1 (2006): 139-177. <http://eudml.org/doc/282988>.

@article{LaureHelme2006,
abstract = {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.},
author = {Laure Helme-Guizon, Józef H. Przytycki, Yongwu Rong},
journal = {Fundamenta Mathematicae},
keywords = {graph; knot; Khovanov homology; graph homology; Hochschild homology; torsion},
language = {eng},
number = {1},
pages = {139-177},
title = {Torsion in graph homology},
url = {http://eudml.org/doc/282988},
volume = {190},
year = {2006},
}

TY - JOUR
AU - Laure Helme-Guizon
AU - Józef H. Przytycki
AU - Yongwu Rong
TI - Torsion in graph homology
JO - Fundamenta Mathematicae
PY - 2006
VL - 190
IS - 1
SP - 139
EP - 177
AB - 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.
LA - eng
KW - graph; knot; Khovanov homology; graph homology; Hochschild homology; torsion
UR - http://eudml.org/doc/282988
ER -