Secondary power operations and the Brown-Peterson spectrum at the prime 2

Tyler Lawson

doi:10.4007/ANNALS.2018.188.2.3

Secondary power operations and the Brown-Peterson spectrum at the prime 2

Tyler Lawson

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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 subalgebrais 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 forany n ≥ 12, answering a question of May in the negative.

Original language	English (US)
Pages (from-to)	513-576
Number of pages	64
Journal	Annals of Mathematics
Volume	188
Issue number	2
DOIs	https://doi.org/10.4007/ANNALS.2018.188.2.3
State	Published - 2018

Bibliographical note

Funding Information:
Keywords: structured ring spectra, secondary operations, Brown-Peterson spectrum AMS Classification: Primary: 55P43. The author was partially supported by NSF grant 1610408. ©c 2018 Department of Mathematics, Princeton University.

Publisher Copyright:
© 2018 Department of Mathematics, Princeton University.

Keywords

Brown-Peterson spectrum
Secondary operations
Structure dring spectra

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title = "Secondary power operations and the Brown-Peterson spectrum at the prime 2",

abstract = "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 subalgebrais not closed under it. This allows us to conclude that the 2-primary Brown- Peterson spectrum does not admit the structure of an En-algebra forany n ≥ 12, answering a question of May in the negative.",

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N1 - Funding Information: Keywords: structured ring spectra, secondary operations, Brown-Peterson spectrum AMS Classification: Primary: 55P43. The author was partially supported by NSF grant 1610408. ©c 2018 Department of Mathematics, Princeton University. Publisher Copyright: © 2018 Department of Mathematics, Princeton University.

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N2 - 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 subalgebrais not closed under it. This allows us to conclude that the 2-primary Brown- Peterson spectrum does not admit the structure of an En-algebra forany n ≥ 12, answering a question of May in the negative.

AB - 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 subalgebrais not closed under it. This allows us to conclude that the 2-primary Brown- Peterson spectrum does not admit the structure of an En-algebra forany n ≥ 12, answering a question of May in the negative.

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KW - Structure dring spectra

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ER -

Secondary power operations and the Brown-Peterson spectrum at the prime 2

Abstract

Bibliographical note

Keywords

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