Algebraic & Geometric Topology

Units of equivariant ring spectra

Rekha Santhanam

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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

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

Received: 27 December 2009
Revised: 1 February 2011
Accepted: 21 February 2011
First available in Project Euclid: 19 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P91: Equivariant homotopy theory [See also 19L47] 55P42: Stable homotopy theory, spectra
Secondary: 55P47: Infinite loop spaces 55P48: Loop space machines, operads [See also 18D50]

equivariant infinite loop space equivariant $\Gamma$–space equivariant spectra


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

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