Uniqueness of E_∞ structures for connective covers

2005/06/21 by Andrew Baker, Baker, Andrew, Birgit Richter +1
Mathematics · #55N15 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N15 #msc:55P43

paper · pdf · doi:10.48550/arxiv.math/0506422

Revised version

openalex publication_date 2005/06/21 · arxiv created 2006/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We refine our earlier work on the existence and uniqueness of E-infinity structures on K-theoretic spectra to show that at each prime p, the connective Adams summand has an essentially unique structure as a commutative S-algebra. For the p-completion we show that the McClure-Staffeldt model for it is equivalent as an E-infinity ring spectrum to the connective cover of the periodic Adams summand. We establish Bousfield equivalence between the connective cover, c(E_n), of the Lubin-Tate spectrum E_n and BP<n> and propose c(E_n) as an E-infinity approximation to the latter.

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