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5 votes

Adem relations of Steenrod square without modding out the coboundaries

Theorem 3.1 in Peter May's "A General Algebraic Approach to Steenrod Operations" gives a better behaved definition for $Sq^k(x)$ for (co)chains $x$ which are not assumed to be cocycles. It probably …
Robert Bruner's user avatar
12 votes
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Ádem relations for the Steenrod and the Dyer–Lashof algebra

See Peter May's "A General Algebraic approach to Steenrod Operations". Both arise from considering the inclusion of a Sylow $p$-subgroup into $\Sigma_{p^2}$. There is a universal $\mathbb{Z}$-index …
Robert Bruner's user avatar
11 votes

understanding Steenrod squares

If I interpret the request a bit differently, I would say that the Steenrod operations in the cohomology of a spectrum tell you about the attachments of the cells. If $Sq^1 x = y$, then a cell dual t …
Robert Bruner's user avatar
18 votes

understanding Steenrod squares

I give an intuitive account of the origin of Steenrod operations in cohomology, Dyer-Lashof operations in homology of infinite loop spaces, and Steenrod operations in the cohomology of cocommutative H …
Robert Bruner's user avatar