Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Rational $O(2)$-equivariant spectra

Pages: 225 – 252

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a12


David Barnes (School of Mathematics and Physics, Pure Mathematics Research Centre, University Road, Queen’s University Belfast, United Kingdom)


The category of rational $O(2)$-equivariant cohomology theories has an algebraic model $\mathcal{A}(O(2))$, as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational $O(2)$-equivariant spectra and the derived category of the abelian model $D\mathcal{A}(O(2))$. In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.


equivariant spectrum, model category, right Bousfield localisation, ring spectrum, algebraic model

2010 Mathematics Subject Classification

55N91, 55P42, 55P60

Published 6 June 2017