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

Wang, Guozhen; Xu, Zhouli

doi:10.2140/agt.2018.18.3887

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Some extensions in the Adams spectral sequence and the $51$–stem

Guozhen Wang and Zhouli Xu

Algebraic & Geometric Topology 18 (2018) 3887–3906

DOI: 10.2140/agt.2018.18.3887

Abstract

We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the $2$ –primary part of $π_{51}$ is $ℤ ∕ 8 \oplus ℤ ∕ 8 \oplus ℤ ∕ 2$ . This was the last unsolved $2$ –extension problem left by the recent work of Isaksen and the authors through the $61$ –stem.

The proof of this result uses the $R P^{\infty}$ technique, which was introduced by the authors to prove $π_{61} = 0$ . This paper advertises this technique through examples that have simpler proofs than in our previous work.

Keywords

Adams spectral sequence, Atiyah–Hirzebruch spectral sequence

Mathematical Subject Classification 2010

Primary: 55Q40

References

Publication

Received: 26 July 2017

Revised: 12 July 2018

Accepted: 3 August 2018

Published: 11 December 2018

Authors

Guozhen Wang
Shanghai Center for Mathematical Sciences Fudan University Shanghai China

Zhouli Xu
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States

Volume 18, issue 7 (2018)