The $C_{2^n}$ Borel dual Steenrod algebra

TL;DR

This paper extends the computation of the $G$-equivariant Borel dual Steenrod algebra from the group $C_2$ to all cyclic groups of order $2^n$, providing a broader understanding in algebraic topology.

Contribution

It generalizes the Hu-Kriz computation of the Borel dual Steenrod algebra from $C_2$ to all $C_{2^n}$ groups, expanding the scope of equivariant cohomology calculations.

Findings

Extended the algebraic computation to all $C_{2^n}$ groups.

Provided explicit descriptions of the algebra structure for larger cyclic groups.

Simplified the understanding of equivariant Steenrod algebra in characteristic 2.

Abstract

In this very short note, we expand the Hu-Kriz computation of the $G$-equivariant Borel dual Steenrod algebra in characteristic $2$, from the group $G=C_2$ to all power-$2$ cyclic groups $G=C_{2^n}$.