Stable Homotopy Seminar, 18: The Steenrod Algebra (Liam Keenan)
Channel: Paul VanKoughnett
Date: 05/07/2021

Liam defines the Steenrod algebra, as the endomorphisms of the Eilenberg-MacLane spectrum HF_p. This naturally acts on the mod p cohomology of any space (or spectrum), and we look at the example of the mod 2 cohomology of RP^infinity. He states some of its fundamental properties allowing us to calculate with it, such as its relation with the cup product and Bockstein, the Adem relations, and the Serre-Cartan basis in terms of admissible sequences. As an application, Liam proves that the Moore spectrum S/2 does not admit a unital multiplication.


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This is part of the stable homotopy learning seminar organized by Paul VanKoughnett. For notes and more, visit https://www.math.purdue.edu/~pvankoug/spectra/index.html.