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The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown–Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown–Peterson spectrum does not admit the structure of an $E_n$-algebra for any $n \geq 12$, answering a question of May in the negative.
@article{10_4007_annals_2018_188_2_3,
author = {Tyler Lawson},
title = {Secondary power operations and the {Brown{\textendash}Peterson} spectrum at the prime $2$},
journal = {Annals of mathematics},
pages = {513--576},
publisher = {mathdoc},
volume = {188},
number = {2},
year = {2018},
doi = {10.4007/annals.2018.188.2.3},
mrnumber = {3862947},
zbl = {06921186},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.3/}
}
TY - JOUR AU - Tyler Lawson TI - Secondary power operations and the Brown–Peterson spectrum at the prime $2$ JO - Annals of mathematics PY - 2018 SP - 513 EP - 576 VL - 188 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.3/ DO - 10.4007/annals.2018.188.2.3 LA - en ID - 10_4007_annals_2018_188_2_3 ER -
%0 Journal Article %A Tyler Lawson %T Secondary power operations and the Brown–Peterson spectrum at the prime $2$ %J Annals of mathematics %D 2018 %P 513-576 %V 188 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.3/ %R 10.4007/annals.2018.188.2.3 %G en %F 10_4007_annals_2018_188_2_3
Tyler Lawson. Secondary power operations and the Brown–Peterson spectrum at the prime $2$. Annals of mathematics, Tome 188 (2018) no. 2, pp. 513-576. doi: 10.4007/annals.2018.188.2.3
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