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arXiv · 1707.01620

Some extensions in the Adams spectral sequence and the 51-stem

Guozhen Wang·Zhouli Xu
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Abstract

We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $\pi_{51}$ is $\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus\mathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (\cite{Isa1}, \cite{IX}, \cite{WX1}) through the 61-stem. The proof of this result uses the $RP^\infty$ technique, which was introduced by the authors in \cite{WX1} to prove $\pi_{61}=0$. This paper advertises this method through examples that have simpler proofs than in \cite{WX1}.

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Guozhen Wang, Zhouli Xu. 2017-07-06. Some extensions in the Adams spectral sequence and the 51-stem. https://doi.org/10.2140/agt.2018.18.3887

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