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The methods of abstract simplicial homology and cohomology are reviewed andapplied to the topology of electrical networks. Kirchhoffs laws of electricalcircuits are shown to be manifestly homological in their origins. Since theyare based in conservation laws, the geometric realization of abstractsimplicial complexes is then reviewed and applied to the case of mechanicalnetworks. The equilibrium condition for statics, the conservation laws forclosed systems, and the balance principles for open systems are then shown toadmit homological formulations.

Homology, equilibrium, and conservation laws I: Discrete systems of points