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

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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.

Original languageEnglish (US)
Pages (from-to)513-576
Number of pages64
JournalAnnals of Mathematics
Volume188
Issue number2
DOIs
StatePublished - 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.

Keywords

  • Brown-Peterson spectrum
  • Secondary operations
  • Structure dring spectra

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