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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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 $BP\langle n\rangle$.


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Additional Information

Andrew Baker
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
MR Author ID: 29540
ORCID: 0000-0002-9369-7702
Email: a.baker@maths.gla.ac.uk

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

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