Algebraic & Geometric Topology

Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

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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

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

Keywords
equivariant stable homotopy category model category rigidity

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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