Subalgebras of the $\mathbb{Z}/2$-equivariant Steenrod algebra

Abstract

International audienceThe aim of this paper is to study sub-algebras of the Z/2-equivariant Steenrod algebra (for cohomology with coefficients in the constant Mackey functor F 2) which come from quotient Hopf algebroids of the Z/2-equivariant dual Steenrod algebra. In particular, we study the equivariant counterpart of profile functions, exhibit the equivariant analogues of the classical A(n) and E(n) and show that the Steenrod algebra is free as a module over these

Real motivic and C2‐equivariant Mahowald invariants

“…Proposition A.1 [29,Proposition 6.2] (see also [53,Proposition 2.13]). The Bredon cohomology of a point with coefficients in F 2 is given by…”

“…We have now recalled enough background to discuss subalgebras of the C 2 -equivariant Steenrod algebra and its dual. This discussion was initiated by Ricka [53], who translated certain profile function techniques of Margolis [43] to the C 2 -equivariant setting in order to study certain quotient Hopf algebroids of A C2 * * . We closely follow [53,Section 5] for the remainder of the subsection.…”

“…This discussion was initiated by Ricka [53], who translated certain profile function techniques of Margolis [43] to the C 2 -equivariant setting in order to study certain quotient Hopf algebroids of A C2 * * . We closely follow [53,Section 5] for the remainder of the subsection. A profile function is minimal if for all i, n 0, τ 2 n i ∈ I(h, k) if and only if n k(i).…”

The cohomology of C2-equivariant 𝒜(1) and the homotopy of koC2

“…Proof. According to [Ri,Corollary 6.19], we have H * , * C2 (kR) ∼ = A C2 //E C2 (1). Since η induces the trivial map on equivariant cohomology, the sequence (10.1) induces a short exact sequence…”

Equivariant stable homotopy theory

“…Example 5. Ricka extended the Hu-Kriz computation of the dual Steenrod algebra for F 2 , and showed that HF 2 has free HF 2 -homology [28], [15].…”