Algebraic & Geometric Topology

Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P42: Stable homotopy theory, spectra 55P91: Equivariant homotopy theory [See also 19L47]
Secondary: 18G55: Homotopical algebra

equivariant stable homotopy category model category rigidity


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

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