We develop a diagrammatic categorification of the polynomial ring ℤ[x]. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xⁿ and standard modules to (x-1)ⁿ in the Grothendieck ring.
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...
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