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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A lower bound for coherences on the Brown–Peterson spectrum

Birgit Richter

Algebraic & Geometric Topology 6 (2006) 287–308

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 2000
Primary: 55P43
Secondary: 13D03
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Publication
Received: 25 May 2005
Revised: 17 November 2005
Accepted: 14 February 2006
Published: 26 February 2006
Authors
Birgit Richter
Fachbereich Mathematik der Universität Hamburg
Bundesstraße 55
20146 Hamburg
Germany
http://www.math.uni-hamburg.de/home/richter/