Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Published electronically: November 2, 2007
MathSciNet review: 2358512
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55P43, 55N15, 19L41

Retrieve articles in all journals with MSC (2000): 55P43, 55N15, 19L41


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: http://dx.doi.org/10.1090/S0002-9939-07-08984-8
PII: S 0002-9939(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