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A lower bound for coherences on the Brown-Peterson spectrum

Birgit Richter
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Abstract

We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP, at a given prime p and prove that it is at least (2p^2 + 2p - 2)-homotopy commutative. We give a proof based on Dyer-Lashof operations that BP cannot be a Thom spectrum associated to n-fold loop maps to BSF for n=4 at 2 and n=2p+4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson-Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K-theory.

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Birgit Richter. 2009-02-27. A lower bound for coherences on the Brown-Peterson spectrum. https://doi.org/10.2140/agt.2006.6.287

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