HPT and cocyclic operations (Q2570230)

The investigation of the relationship between cohomology operations and simplicial cochain operations was initiated by \textit{L. Kristensen} and \textit{I. Madsen} [Math. Scand. 20, 119--130 (1967; Zbl 0166.18902)] and some applications were given in [\textit{S. Klaus}, Cah. Topologie Géom. Différ. Catégoriques 42, 261--284 (2001; Zbl 1003.55005)]. The aim of this paper is to study cocyclic operations from the algorithmic perspective given by homological perturbation theory. More precisely, the authors give a method for obtaining explicit formulae for cocyclic operations. The case of Steenrod and Adem cohomology operations are treated by examples.