2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111561We introduce $Δ$-groups and show how they fit in the context of lattice field theory. To a manifold $M$ we associate a $Δ$-group $Γ(M)$. We define the symmetric cohomology $HS^n(G,A)$ of a group $G$ with coefficients in a $G$-module $A$. The $Δ$-group $Γ(M)$ is determined by the action of $π_1(M)$ on $π_2(M)$ and an element of $HS^3(π_1(M),π_2(M))$.18 pagesGeometric TopologyAlgebraic Topologytext