Who is credited with the creation/invention of the cup product? Wikipedia gives credit to several but I wasn't able to confirm.
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6$\begingroup$ Would be better suited at History of Science and Mathematics SE $\endgroup$– WojowuCommented Jan 10, 2019 at 18:00
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6$\begingroup$ This is described in Dieudonné's magisterial "A History of Algebraic and Differential Topology, 1900 - 1960". See chapter 4, pages 81--85. The answer is a bit complicated because the notion was first introduced in simplicial cohomology and then later in singular cohomology (after the latter was invented, of course!). $\endgroup$– Danny RubermanCommented Jan 10, 2019 at 18:56
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$\begingroup$ Thank you Prof. Ruberman! @Wojowu, I'll be sure to post questions like this in the correct forum. Thanks for the clarification $\endgroup$– YDPCommented Jan 10, 2019 at 21:21
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1 Answer
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W. S. Massey gives a rather detailed account in his essay, "A history of cohomology theory" (in History of Topology, edited by I. M. James, North Holland, 2006). The initial idea was due to Alexander and Kolmogoroff, apparently simultaneously and independently, but there were some "bugs" in the original version. Čech and Whitney, in separate papers, cleaned up the definition (Čech for finite simplicial complexes, Whitney more generally for finite cell complexes).
answered Jan 10, 2019 at 23:25
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$\begingroup$ Addendum: According to the account in Keith Kendig's book Never a Dull Moment, Čech and Whitney did not work entirely independently, although Kendig does not explain in detail the extent of their collaboration, nor why they chose to write two separate papers. $\endgroup$ Commented Jan 14, 2019 at 2:40