Volume 16, issue 4 (2016)

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Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

Algebraic & Geometric Topology 16 (2016) 2159–2227

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.

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equivariant stable homotopy category, model category, rigidity
Mathematical Subject Classification 2010
Primary: 55P42, 55P91
Secondary: 18G55
Received: 19 June 2015
Accepted: 4 August 2015
Published: 12 September 2016
Irakli Patchkoria
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen