From 3-algebras to Δ-groups and symmetric cohomology

We introduce Δ-groups and show how they fit in the context of lattice field theory. To a topological space M we associate a Δ-group Γ(M). We define the symmetric cohomology HSn(G,A) of a group G with coefficients in a G-module A. The Δ-group Γ(M) is determined by the action of π1(M) on π2(M) and an element of HS3(π1(M),π2(M)).