Uniqueness of $E_\infty$ structures for connective covers

Details Uniqueness of $E_\infty$ structures for connective covers Uniqueness of $E_\infty$ structures for connective covers

2005-06-21

arxiv.org/abs/math/0506422v2

Mathematics

Algebraic Topology

Revised version

Scientific paper

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 and propose c(E_n) as an E-infinity approximation to the latter.

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