A lower bound for coherences on the Brown–Peterson spectrum

Richter, Birgit

doi:10.2140/agt.2006.6.287

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A lower bound for coherences on the Brown–Peterson spectrum

Birgit Richter

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, $B P$ , at a given prime $p$ and prove that it is at least $(2 p^{2} + 2 p - 2)$ –homotopy commutative. We give a proof based on Dyer–Lashof operations that $B P$ cannot be a Thom spectrum associated to $n$ –fold loop maps to $B S F$ for $n = 4$ at $2$ and $n = 2 p + 4$ 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/

Volume 6, issue 1 (2006)