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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
Abstract

We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2–primary part of π51 is 8 8 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 RP technique, which was introduced by the authors to prove π61 = 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