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2016 On the Adams isomorphism for equivariant orthogonal spectra
Holger Reich, Marco Varisco
Algebr. Geom. Topol. 16(3): 1493-1566 (2016). DOI: 10.2140/agt.2016.16.1493


We give a natural construction and a direct proof of the Adams isomorphism for equivariant orthogonal spectra. More precisely, for any finite group G, any normal subgroup N of G, and any orthogonal G–spectrum X, we construct a natural map A of orthogonal G N–spectra from the homotopy N–orbits of X to the derived N–fixed points of X, and we show that A is a stable weak equivalence if X is cofibrant and N–free. This recovers a theorem of Lewis, May and Steinberger in the equivariant stable homotopy category, which in the case of suspension spectra was originally proved by Adams. We emphasize that our Adams map A is natural even before passing to the homotopy category. One of the tools we develop is a replacement-by-Ω–spectra construction with good functorial properties, which we believe is of independent interest.


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Holger Reich. Marco Varisco. "On the Adams isomorphism for equivariant orthogonal spectra." Algebr. Geom. Topol. 16 (3) 1493 - 1566, 2016.


Received: 15 September 2014; Revised: 22 July 2015; Accepted: 21 September 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1350.55015
MathSciNet: MR3523048
Digital Object Identifier: 10.2140/agt.2016.16.1493

Primary: 55P42, 55P91

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 3 • 2016
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