On the computability of the p-local homology of twisted cartesian products of Eilenberg-Mac Lane spaces V. ´ Alvarez ∗ J.A. Armario † P. Real ∗ Dpto. de Matem´ atica Aplicada I. Univ. de Sevilla. E-mails: valvarez@euler.fie.us.es, armario@cica.es, real@cica.es Abstract Working in the framework of the Simplicial Topology, a method for calcu- lating the p-local homology of a twisted cartesian product X (π,m,τ,π ′ ,n)= K(π,m) × τ K(π ′ ,n) of Eilenberg-Mac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between the normalized chain complex of X and a free DGA-module of finite type M , via homological perturbation. If X is a commutative simplicial group (being its inner product the natural one of the cartesian product of K(π,m) and K(π ′ ,n)), then M is a DGA-algebra. Finally, in the special case K(π, 1)  → X p → K(π ′ ,n), we prove that M can be a small twisted tensor product. 1 Introduction In Simplicial Topology [14], fibre bundles simplify its own structure since they can be considered as twisted cartesian products (TCPs) of two simplicial sets (fibre) × τ (base), where the function τ produces a “torsion” on the 0-face of the cartesian product. An example of principal TCP is X (π,m,τ,π ′ ,n)= K (π,m) × τ K (π ′ ,n), where K (π,m) and K (π ′ ,n) are Eilenberg-Mac Lane spaces. We are interested here in a PTCP of the form X (π,m,τ,π ′ ,n) where π and π ′ are finitely generated abelian groups and m, n ∈ N. More precisely, we want to calculate the p-local homology of X . Our approach is based essentially in the use of techniques * Facultad de Inform´atica y Estad´ ıstica. Avda. Reina Mercedes S.N. 41012, Sevilla (Spain). † Escuela Universitaria de Ingenier´ ıa T´ ecnica Agr´ ıcola. Ctra. Utrera Km. 1, 41013, Sevilla (Spain). First author is supported by a grant from the Junta de Andaluc ´ ia 1