  The methods of abstract simplicial homology and cohomology are reviewed and
applied to the topology of electrical networks. Kirchhoffs laws of electrical
circuits are shown to be manifestly homological in their origins. Since they
are based in conservation laws, the geometric realization of abstract
simplicial complexes is then reviewed and applied to the case of mechanical
networks. The equilibrium condition for statics, the conservation laws for
closed systems, and the balance principles for open systems are then shown to
admit homological formulations.
