#### Volume 16, issue 4 (2016)

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Rigidity in equivariant stable homotopy theory

### Irakli Patchkoria

Algebraic & Geometric Topology 16 (2016) 2159–2227
##### 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