An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincaré algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds.
Doran, Charles F.; Iga, Kevin M.; and Landweber, Gregory D., "An application of cubical cohomology to Adinkras and supersymmetry representations" (2017). Pepperdine University, All Faculty Open Access Publications. Paper 179.