Algebraic & Geometric Topology

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

Guozhen Wang and Zhouli Xu

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We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2 –primary part of π 5 1 is 8 8 2 . This was the last unsolved 2 –extension problem left by the recent work of Isaksen and the authors through the 6 1 –stem.

The proof of this result uses the R P technique, which was introduced by the authors to prove π 6 1 = 0 . This paper advertises this technique through examples that have simpler proofs than in our previous work.

Article information

Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3887-3906.

Received: 26 July 2017
Revised: 12 July 2018
Accepted: 3 August 2018
First available in Project Euclid: 18 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55Q40: Homotopy groups of spheres

Adams spectral sequence Atiyah–Hirzebruch spectral sequence


Wang, Guozhen; Xu, Zhouli. Some extensions in the Adams spectral sequence and the $51$–stem. Algebr. Geom. Topol. 18 (2018), no. 7, 3887--3906. doi:10.2140/agt.2018.18.3887.

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