Steenrod operations and A-module extensions

Robert Bruner; Christian Nassau; Sean Tilson

paper

Steenrod operations and A-module extensions

arXiv:1909.03117

Abstract

Explicit extensions representing cocycles $x \in E x t_{A}^{s, t} (F_{2}, F_{2})$ are useful in calculating Steenrod operations $S q^{i} : E x t_{A}^{s, t} (F_{2}, F_{2}) ⟶ E x t_{A}^{s + i, 2 t} (F_{2}, F_{2})$ by a method devised by the second author. This can be used to identify explicit cocycles in the minimal resolutions produced by the first author's computer programs, and this information is useful in determining differentials in the Adams spectral sequence.

Added higher diagonals for f_0, establishing our claims about Steenrod operations on this element. Corrected minor typos. Improved exposition in a few places