From 3-algebras to $Δ$-Groups

Abstract

We 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 $HS^3(π_1(M),π_2(M))$.