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Motivation and history of singular homology

Regarding singular homology proper, its main development occurred in the 1930s and 1940s with Lefschetz and Eilenberg figuring prominently. For this history, Dieudonné's "A History of Algebraic ...
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Motivation and history of singular homology

Poincare's original papers, Analysis situs and 5 supplements to it, contain relatively few formulas, make a good reading, and explain his motivation. If you can read French. Another good source is H. ...
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History of cohomology theory

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 ...
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