A lower bound for coherences on the Brown-Peterson spectrum

Details A lower bound for coherences on the Brown-Peterson spectrum A lower bound for coherences on the Brown-Peterson spectrum

2005-04-15

arxiv.org/abs/math/0504322v2

Algebr. Geom. Topol. 6 (2006) 287-308

Mathematics

Algebraic Topology

This is the version published by Algebraic & Geometric Topology on 26 February 2006

Scientific paper

10.2140/agt.2006.6.287

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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