I have read that one of the origins of the theory of (co)homology is the study of electrical circuits by Poincare. I'd like to know more about that. Could someone sugest any reference on this subject?
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2$\begingroup$ If you scroll down a little ways to "Chain Complexes from Circuits" here: ncatlab.org/johnbaez/show/Circuit+theory+I you will see some mention of a paper by Weyl on the subject. $\endgroup$– J126Mar 30, 2015 at 2:04
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John Baez in "Circuit Theory" states: "In 1923, Hermann Weyl published a paper in Spanish which described electrical circuits in terms of the homology and cohomology of graphs (W). In this approach, Kirchhoff’s voltage and current laws simply say that voltage is a 1-coboundary and current is a 1-cocycle. Furthermore, the electrical resistances labelling edges of the graphs put an inner product on the space of 1-chains, allowing us to identify them with 1-cochains. Ohm’s law then says that voltage may then be identified with the current." http://ncatlab.org/johnbaez/show/Circuit+theory+I
The Weyl paper is H. Weyl, Repartición de corriente en una red conductora, Rev. Mat. Hisp. Amer. 5 (1923), 153-164. http://math.ucr.edu/home/baez/weyl1923.pdf
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$\begingroup$ although it all sounds very lofty and elegant, I can assure you that it has not contributed anything to circuit theory. $\endgroup$– structJul 4, 2022 at 17:02
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An additional reference is "Graphs and Networks. The Picard-Lefschetz Theory and Feynman Integrals" by Lefschetz . Chapter electrical circuit
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$\begingroup$ And also Ziedler Electrical Circuits as a Paradigm in Homology and Cohomology $\endgroup$– BaudotMar 23, 2017 at 13:51
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$\begingroup$ download.springer.com/static/pdf/265/…*~hmac=55cfb40bb8003b185b862d15ea2bc9068daf69137b4dc9bfc3737db9ad50f389 $\endgroup$– BaudotMar 23, 2017 at 13:52