Couniversal spaces which are equivariant commutative ring spectra

TL;DR

This paper characterizes couniversal spaces whose suspension spectra form equivariant commutative ring spectra, linking their cofamilies and operad actions to their algebraic and topological properties.

Contribution

It provides a precise criterion for when couniversal spaces yield equivariant commutative ring spectra based on their cofamilies and operad actions.

Findings

Couniversal spaces with cofamilies closed under finite index subgroups produce equivariant commutative ring spectra.

Such spaces admit an action of an equivariant E infinity operad.

The characterization connects algebraic properties of spaces with their spectral and operadic structures.

Abstract

The note identifies which which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring G-spectra for a compact Lie group G. These are precisely those whose cofamily is closed under passage to finite index subgroups. Equivalently these are the couniversal spaces admitting an action of an equivariant E infinity operad.