The Fiber of $S{q}^n$

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.

arXiv commentTo 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"