Algebraic & Geometric Topology

A lower bound for coherences on the Brown–Peterson spectrum

Birgit Richter

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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+2p2)–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.

Article information

Algebr. Geom. Topol., Volume 6, Number 1 (2006), 287-308.

Received: 25 May 2005
Revised: 17 November 2005
Accepted: 14 February 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)

structured ring spectra Brown-Peterson spectrum


Richter, Birgit. A lower bound for coherences on the Brown–Peterson spectrum. Algebr. Geom. Topol. 6 (2006), no. 1, 287--308. doi:10.2140/agt.2006.6.287.

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