## An algebraic model for rational S 1 -equivariant stable homotopy theory,Quart.J.ofMath

Venue: | of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK. E-mail address: j.greenlees@sheffield.ac.uk |

Citations: | 9 - 5 self |

### BibTeX

@INPROCEEDINGS{Shipley_analgebraic,

author = {Brooke Shipley},

title = {An algebraic model for rational S 1 -equivariant stable homotopy theory,Quart.J.ofMath},

booktitle = {of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK. E-mail address: j.greenlees@sheffield.ac.uk},

year = {},

pages = {87--110}

}

### OpenURL

### Abstract

graded objects in A models the whole rational S 1-equivariant stable homotopy theory. That is, we show that there is a Quillen equivalence between dgA and the model category of rational S 1-equivariant spectra, before the quasi-isomorphisms or stable equivalences have been inverted. This implies that all of the higher order structures such as mapping spaces, function spectra and homotopy (co)limits are reflected in the algebraic model. The construction of this equivalence involves calculations with Massey products. In an appendix we show that Toda brackets, and hence also Massey products, are determined by the derived category.

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Citation Context ...ss.: 55P62, 55P91, 55P42, 55N91, 18E30. Research partially supported by an NSF grant. 12 BROOKE SHIPLEY The main new ingredient here is a Morita equivalence for stable model categories considered in =-=[22]-=-, see Section 3. In general, this Morita equivalence models a stable model category with a set of small generators by modules over a ring spectrum (with many objects). For rational stable model catego... |

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Rational S1-equivariant stable homotopy theory, Mem.Amer.Math. Soc. vol 138. no 661
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Citation Context ...n of this equivalence involves calculations with Massey products. In an appendix we show that Toda brackets, and hence also Massey products, are determined by the derived category. 1. Introduction In =-=[5]-=-, Greenlees defined an abelian category A and showed that its derived category is equivalent to the rational T-equivariant stable homotopy category where T is the circle group. We strengthen this resu... |

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