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We study the Mahowald operator $M = langle g_2,h_0^3, - rangle$ in the cohomology of the Steenrod algebra. We show that the operator interacts well with the cohomology of $A(2)$, in both the classical and $mathbb{C}$-motivic contexts. This generalizes previous work of Margolis, Priddy, and Tangora.
We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $underline{mathbb{F}}_p$ and $underline{mathbb{Z}}_{(p)}$, as $underline{mathbb{Z}}_{(p)}$-modules. The $C_p$-spectrum $underline{mathbb{F}}_p otimes u
The Joker is an important finite cyclic module over the mod-$2$ Steenrod algebra $mathcal A$. We show that the Joker, its first two iterated Steenrod doubles, and their linear duals are realizable by spaces of as low a dimension as the instability co
In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the construction in more general homological terms, using group homology and a
Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This paper is
The dual motivic Steenrod algebra with mod $ell$ coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and {O}stv{ae}r over a base field of characteristic $p eq ell$. In the case $p = ell$, we show th