## Algebraic & Geometric Topology

### Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

#### 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 $2$.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2159-2227.

Dates
Received: 19 June 2015
Accepted: 4 August 2015
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895912

Digital Object Identifier
doi:10.2140/agt.2016.16.2159

Mathematical Reviews number (MathSciNet)
MR3546463

Zentralblatt MATH identifier
1356.55006

#### Citation

Patchkoria, Irakli. Rigidity in equivariant stable homotopy theory. Algebr. Geom. Topol. 16 (2016), no. 4, 2159--2227. doi:10.2140/agt.2016.16.2159. https://projecteuclid.org/euclid.agt/1511895912

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