## Algebraic & Geometric Topology

### Units of equivariant ring spectra

Rekha Santhanam

#### Abstract

It is well known that very special $Γ$–spaces and grouplike $E∞$–spaces both model connective spectra. Both these models have equivariant analogues in the case when the group acting is finite. Shimakawa defined the category of equivariant $Γ$–spaces and showed that special equivariant $Γ$–spaces determine positive equivariant spectra. Costenoble and Waner [Trans. Amer. Math. Soc. 326 (1991) 485-505] showed that grouplike equivariant $E∞$–spaces determine connective equivariant spectra.

We show that with suitable model category structures the category of equivariant $Γ$–spaces is Quillen equivalent to the category of equivariant $E∞$–spaces. We define the units of equivariant ring spectra in terms of equivariant $Γ$–spaces and show that the units of an equivariant ring spectrum determines a connective equivariant spectrum.

#### Article information

Source
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1361-1403.

Dates
Revised: 1 February 2011
Accepted: 21 February 2011
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715231

Digital Object Identifier
doi:10.2140/agt.2011.11.1361

Mathematical Reviews number (MathSciNet)
MR2821427

Zentralblatt MATH identifier
1227.55014

#### Citation

Santhanam, Rekha. Units of equivariant ring spectra. Algebr. Geom. Topol. 11 (2011), no. 3, 1361--1403. doi:10.2140/agt.2011.11.1361. https://projecteuclid.org/euclid.agt/1513715231

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