Algebraic & Geometric Topology 6 (2006) 287–308

DOI: 10.2140/agt.2006.6.287

arXiv: math.AT/0504322

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 (2p²+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.

Keywords

structured ring spectra, Brown-Peterson spectrum

Mathematical Subject Classification

Primary: 55P43

Secondary: 13D03

References

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Publication

Received: 25 May 2005
Revised: 17 November 2005
Accepted: 14 February 2006
Published: 26 February 2006

Authors