Volume 11, issue 3 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Units of equivariant ring spectra

Rekha Santhanam

Algebraic & Geometric Topology 11 (2011) 1361–1403
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.

Keywords
equivariant infinite loop space, equivariant $\Gamma$–space, equivariant spectra
Mathematical Subject Classification 2000
Primary: 55P91, 55P42
Secondary: 55P47, 55P48
References
Publication
Received: 27 December 2009
Revised: 1 February 2011
Accepted: 21 February 2011
Published: 17 May 2011
Authors
Rekha Santhanam
Department of Mathematics and Statistics
Indian Institute of Technology, Kanpur
Kanpur UP 208016
India