Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

Couniversal spaces which are equivariantly commutative ring spectra

Pages: 69 – 75

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a5


J.P.C. Greenlees (Warwick Mathematics Institute, Coventry, United Kingdom)


The paper identifies which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring $G$-spectra for a compact Lie group $G$. Equivalently these are the couniversal spaces admitting an action of an $E_{\infty}^G$-operad. We show that they are precisely the couniversal spaces associated to a cofamily whose minimal subgroups are connected.


equivariant ring spectra, commutativity, operad, orthogonal spectra, couniversal space

2010 Mathematics Subject Classification

18D50, 55P91

Received 21 August 2018

Received revised 31 March 2019

Accepted 2 April 2019

Published 30 October 2019