The cohomology of the mod 2 Steenrod algebra

TL;DR

This paper provides a detailed minimal resolution of the mod 2 Steenrod algebra within a specific range, including explicit chain maps and the squaring operation in its cohomology, aiding algebraic topology computations.

Contribution

It offers the first comprehensive minimal resolution and explicit chain maps for the mod 2 Steenrod algebra in the specified range, enhancing computational tools.

Findings

Explicit minimal resolution up to s=128, t=200

Chain maps for each cocycle in the range

Representation of the squaring operation Sq^0

Abstract

A minimal resolution of the mod 2 Steenrod algebra in the range $0 \leq s \leq 128$, $0 \leq t \leq 200$, together with chain maps for each cocycle in that range and for the squaring operation $Sq^0$ in the cohomology of the Steenrod algebra.