Units of equivariant ring spectra

Abstract

It is well known that very special $\Gamma$-spaces and grouplike $\E_\infty$ spaces both model connective spectra. Both these models have equivariant analogues. Shimakawa defined the category of equivariant $\Gamma$-spaces and showed that special equivariant $\Gamma$-spaces determine positive equivariant spectra. Costenoble and Waner showed that grouplike equivariant $\E_\infty$-spaces determine connective equivariant spectra. We show that with suitable model category structures the category of equivariant $\Gamma$-spaces is Quillen equivalent to the category of equivariant $\E_\infty$ spaces. We define the units of equivariant ring spectra in terms of equivariant $\Gamma$-spaces and show that the units of an equivariant ring spectrum determines a connective equivariant spectrum.

More detailed introduction, added appendix C

References in corpus (3)

• Twisted equivariant K-theory with complex coefficients
• Units of ring spectra and Thom spectra
• Continuous functors as a model for the equivariant stable homotopy category

Cited by in corpus (5)

• Units of ring spectra and Thom spectra
• Group completion and units in I-spaces
• Equivariant infinite loop space theory, the space level story
• A short treatise on Equivariant Gamma spaces
• Recognition of commutative algebra spectra through an idempotent quasiadjunction