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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 π51 is ℤ∕8 ⊕ ℤ∕8 ⊕ 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 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
Wang, Guozhen 1 ; Xu, Zhouli 2
@article{10_2140_agt_2018_18_3887,
author = {Wang, Guozhen and Xu, Zhouli},
title = {Some extensions in the {Adams} spectral sequence and the 51{\textendash}stem},
journal = {Algebraic and Geometric Topology},
pages = {3887--3906},
publisher = {mathdoc},
volume = {18},
number = {7},
year = {2018},
doi = {10.2140/agt.2018.18.3887},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3887/}
}
TY - JOUR AU - Wang, Guozhen AU - Xu, Zhouli TI - Some extensions in the Adams spectral sequence and the 51–stem JO - Algebraic and Geometric Topology PY - 2018 SP - 3887 EP - 3906 VL - 18 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3887/ DO - 10.2140/agt.2018.18.3887 ID - 10_2140_agt_2018_18_3887 ER -
%0 Journal Article %A Wang, Guozhen %A Xu, Zhouli %T Some extensions in the Adams spectral sequence and the 51–stem %J Algebraic and Geometric Topology %D 2018 %P 3887-3906 %V 18 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3887/ %R 10.2140/agt.2018.18.3887 %F 10_2140_agt_2018_18_3887
Wang, Guozhen; Xu, Zhouli. Some extensions in the Adams spectral sequence and the 51–stem. Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3887-3906. doi: 10.2140/agt.2018.18.3887
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