Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 1 (2006), 287-308.
A lower bound for coherences on the Brown–Peterson spectrum
We provide a lower bound for the coherence of the homotopy commutativity of the Brown–Peterson spectrum, , at a given prime and prove that it is at least –homotopy commutative. We give a proof based on Dyer–Lashof operations that cannot be a Thom spectrum associated to –fold loop maps to for at and 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-–theory.
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
Permanent link to this document
Digital Object Identifier
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.)
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