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I saw this post. And I already posted it on Math stack exchange, but since someone recommended this site, I'm refining it and posting it again. And I understand that the mathematical object called cohomology came from Poincaré duality. But I would like to know the details of the history of cohomology itself. So, if you know, I would appreciate it if you could leave an answer. Or, I would appreciate it if you could recommend a book related to the history of cohomology with as few formulas as possible.

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Cohomology theories were introduced independently by A. Kolmogorov, Ueber die Dualitat im Aufbau der kombinatorischen Topologie, Mat. Sbornik, vol. 1, 1936, 97-102,

and by J. W. Alexander, On the chains of a complex and their duals, Proc. Nat. Acad. Sci, 21, 1935, 509-512, complete exposition in A.. of Math., 37, 1936, 698-708.

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  • $\begingroup$ Of course, one might mention Gauss-Green-Stokes as precursors. $\endgroup$ Feb 8 at 21:45
  • $\begingroup$ @Paul Garrett: Yes, and especially Maxwell's Treatise on electricity and magnetism. But formal definition is due to Alexander and Kolmogorov. $\endgroup$ Feb 9 at 14:01

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