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Uniqueness of $ E_\infty$ structures for connective covers


Authors: Andrew Baker and Birgit Richter
Journal: Proc. Amer. Math. Soc. 136 (2008), 707-714
MSC (2000): Primary 55P43, 55N15; Secondary 19L41
DOI: https://doi.org/10.1090/S0002-9939-07-08984-8
Published electronically: November 2, 2007
MathSciNet review: 2358512
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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 $ \mathit{BP}\langle n\rangle$.


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Additional Information

Andrew Baker
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Email: a.baker@maths.gla.ac.uk

Birgit Richter
Affiliation: Department Mathematik der Universität Hamburg, 20146 Hamburg, Germany
Email: richter@math.uni-hamburg.de

DOI: https://doi.org/10.1090/S0002-9939-07-08984-8
Received by editor(s): October 10, 2006
Received by editor(s) in revised form: October 25, 2006
Published electronically: November 2, 2007
Additional Notes: The first author thanks the Max-Planck Institute and the mathematics department in Bonn.
The second author was partially supported by the Strategisk Universitetsprogram i Ren Matematikk (SUPREMA) of the Norwegian Research Council.
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society

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