English

The Fiber of $Sq^n$

Algebraic Topology 2026-05-01 v2

Abstract

A colleague asked about the Adams filtrations of the homotopy classes in the homotopy of the fiber of a particular map between GEMs. The theorem proved in arXiv:2105.02601v3 [math.AT] proves to be effective in answering this (Theorem 4.4). We show that this and some related Adams spectral sequences all collapse at E3E_3 and we determine the value of E3=EE_3 = E_\infty. Notably, we do not need to determine the cohomology of the fiber or the E2E_2 term of the Adams spectral sequence to do this.

Keywords

Cite

@article{arxiv.2601.04028,
  title  = {The Fiber of $Sq^n$},
  author = {Robert R. Bruner},
  journal= {arXiv preprint arXiv:2601.04028},
  year   = {2026}
}

Comments

To appear in HHA sometime in spring 2027. No mathematical changes. Minor improvements in exposition and additional references. Ignore HHA 'boilerplate' such as "communicated by Bill Murray"