Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

Commutative Γ-rings do not model all commutative ring spectra

Pages: 189 – 194

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a9

Author

Tyler Lawson (Department of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)

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.

Keywords

gamma-space; ring spectrum; Dyer-Lashof operation

2010 Mathematics Subject Classification

55P42, 55P43, 55S12

Full Text (PDF format)