Rigidity in equivariant stable homotopy theory

Patchkoria, Irakli

doi:10.2140/agt.2016.16.2159

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Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

Algebraic & Geometric Topology 16 (2016) 2159–2227

DOI: 10.2140/agt.2016.16.2159

Abstract

For any finite group $G$ , we show that the $2$ –local $G$ –equivariant stable homotopy category, indexed on a complete $G$ –universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all “higher-order structure” of the $2$ –local $G$ –equivariant stable homotopy category, such as the equivariant homotopy types of function $G$ –spaces. Our result can be seen as an equivariant version of Schwede’s rigidity theorem at the prime $2$ .

Keywords

equivariant stable homotopy category, model category, rigidity

Mathematical Subject Classification 2010

Primary: 55P42, 55P91

Secondary: 18G55

References

Publication

Received: 19 June 2015

Accepted: 4 August 2015

Published: 12 September 2016

Authors

Irakli Patchkoria
Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark

Volume 16, issue 4 (2016)