Homology, Homotopy and Applications

Commutative Γ-rings do not model all commutative ring spectra

Tyler Lawson

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Abstract

We show that the free E∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that Dyer-Lashof operations of positive degree must vanish on the zero'th homology of such an object.

Article information

Source
Homology Homotopy Appl., Volume 11, Number 2 (2009), 189-194.

Dates
First available in Project Euclid: 27 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296138517

Mathematical Reviews number (MathSciNet)
MR2559641

Zentralblatt MATH identifier
1189.55004

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55S12: Dyer-Lashof operations 55P42: Stable homotopy theory, spectra

Keywords
Gamma-space ring spectrum Dyer-Lashof operation

Citation

Lawson, Tyler. Commutative Γ-rings do not model all commutative ring spectra. Homology Homotopy Appl. 11 (2009), no. 2, 189--194. https://projecteuclid.org/euclid.hha/1296138517


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