Uniqueness of 𝐸_{∞} structures for connective covers

Baker, Andrew; Richter, Birgit

doi:10.1090/S0002-9939-07-08984-8

Uniqueness of $E_\infty$ structures for connective covers
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by Andrew Baker and Birgit Richter PDF

Proc. Amer. Math. Soc. 136 (2008), 707-714 Request permission

Abstract:

We refine our earlier work on the existence and uniqueness of $E_\infty$ structures on $K$-theoretic spectra to show that the connective versions of real and complex $K$-theory as well as the connective Adams summand $\ell$ at each prime $p$ have unique structures as commutative $\mathbb {S}$-algebras. For the $p$-completion $\ell _p$ we show that the McClure-Staffeldt model for $\ell _p$ is equivalent as an $E_\infty$ ring spectrum to the connective cover of the periodic Adams summand $L_p$. We establish a Bousfield equivalence between the connective cover of the Lubin-Tate spectrum $E_n$ and $BP\langle n\rangle$.

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