2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231179$N$-complexes have been argued recently to be algebraic structures relevant to the description of higher spin gauge fields. $N$-complexes involve a linear operator $d$ that fulfills $d^N = 0$ and that defines a generalized cohomology. Some elementary properties of $N$-complexes and the evidence for their relevance to the description of higher spin gauge fields are briefly reviewed.Presented at the International Workshop "Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions" in honour of Michel Dubois-Violette, Orsay, April 8-10, 2008High Energy Physics - Theorytext