The Fiber of $Sq^n$

Robert R. Bruner

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arXiv · 2601.04028

The Fiber of $Sq^n$

Robert R. Bruner

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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 $E_3$ and we determine the value of $E_3 = E_\infty$. Notably, we do not need to determine the cohomology of the fiber or the $E_2$ term of the Adams spectral sequence to do this.

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Robert R. Bruner. 2026-01-07. The Fiber of $Sq^n$. https://arxiv.org/abs/2601.04028

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