English

Steenrod operations and A-module extensions

Algebraic Topology 2020-08-03 v3

Abstract

Explicit extensions representing cocycles xExtAs,t(F2,F2)x \in Ext_{A}^{s,t}(F_2,F_2) are useful in calculating Steenrod operations Sqi:ExtAs,t(F2,F2)ExtAs+i,2t(F2,F2)Sq^i : Ext_{A}^{s,t}(F_2,F_2) \longrightarrow Ext_{A}^{s+i,2t}(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.

Cite

@article{arxiv.1909.03117,
  title  = {Steenrod operations and A-module extensions},
  author = {Robert Bruner and Christian Nassau and Sean Tilson},
  journal= {arXiv preprint arXiv:1909.03117},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T11:08:14.374Z