Rational O(2)-Equivariant Spectra

TL;DR

This paper establishes a Quillen equivalence between the homotopy category of rational O(2)-equivariant spectra and an algebraic model, extending previous categorical equivalences to a model category level.

Contribution

It lifts the known algebraic model equivalence to a Quillen equivalence of model categories, compatible with the Adams sequence.

Findings

Established a Quillen equivalence between spectra and algebraic model

Extended categorical equivalence to model category level

Ensured compatibility with Adams short exact sequence

Abstract

The category of rational O(2)-equivariant cohomology theories has an algebraic model 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 DA(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.