Torsion in Graph Homology

2005/07/12 by Helme-Guizon, Laure, Przytycki, Jozef H., Rong, Yongwu · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0507245

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 torsions. When the underlying algebra is ℤ[x]/(x²), we determine precisely those graphs whose cohomology contains torsion. For a larger class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. The ideas of this paper could potentially be used to predict the Khovanov-Rozansky sl(m) homology of knots (in particular (2,n) torus knots). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.

Cited by

• New torsion patterns in Khovanov homology

Related

• Search for Torsion in Khovanov Homology
• Torsion in thin regions of Khovanov homology
• Hyperbolic Knots and Torsion in Khovanov Homology
• Torsion in Khovanov homology of homologically thin knots
• On the first group of the chromatic cohomology of graphs