## Algebraic & Geometric Topology

### A lower bound for coherences on the Brown–Peterson spectrum

Birgit Richter

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1513796513

Digital Object Identifier
doi:10.2140/agt.2006.6.287

Mathematical Reviews number (MathSciNet)
MR2199461

Zentralblatt MATH identifier
1095.55005

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796513

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