Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

Commutative Γ-rings do not model all commutative ring spectra

Pages: 189 – 194

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


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


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.


gamma-space, ring spectrum, Dyer-Lashof operation

2010 Mathematics Subject Classification

55P42, 55P43, 55S12

Published 1 January 2009