Comparative analysis of AWES under topological criteria has barely begun, with just a few scattered references in AWE literature, mostly dealing with topological sub-spaces. System Topologies in AWE vary greatly, and are just as critical as System Geometries.

Consider the power kite in its inflated state as a Euclidian object. Packed away in a bag it preserves its topological form (topological stability) but has disappeared into a geometric sub-space. Every AWES architecture has a unique topology. Its increasingly useful to be able to analytically compare AWES topologically, as part of the broader topological revolution in math, physics, and engineering.