# Rational S1-Equivariant Stable Homotopy Theory (Memoirs of the American Mathematical Society, Vol 138, No. 661) download epub

#### by **J. P. C. Greenlees**

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Memoirs of the American Mathematical Society 1999; 289 pp; MSC .

Memoirs of the American Mathematical Society 1999; 289 pp; MSC: Primary 55; Secondary 18; 19; 20. Electronic ISBN: 978-1-4704-0250-1 Product Code: MEMO/138/661. The memoir presents a systematic study of rational (S^1)-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation.

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Rational S-Equivariant Stable Homotopy Theory book. Rational Sp1S-Equivariant Stable Homotopy Theory (Memoirs of the American Mathematical Society). 0821810014 (ISBN13: 9780821810019).

Memoirs of the American Mathematical Society, Volume 138; doi:10.

Published: 1 January 1999. by American Mathematical Society (AMS). in Memoirs of the American Mathematical Society. Memoirs of the American Mathematical Society, Volume 138; doi:10.

author's AMS Memoir & S^1 equivariant homotopy theory Greenlees defined an abelian category A whose derived category is equivalent to the rational S^1-equivariant stable homotopy category whose objects represent rational . .

author's AMS Memoir & S^1 equivariant homotopy theory. and is natural and explicit in terms of sheaves of functions on A. This is Version . of a paper of long genesis (this should be the final version). Greenlees defined an abelian category A whose derived category is equivalent to the rational S^1-equivariant stable homotopy category whose objects represent rational S^1-equivariant cohomology theories. We show that in fact the model category of differential graded objects in A (dgA) models the whole rational S^1-equivariant stable homotopy theory.

Greenlees defined an abelian category A whose derived category is equivalent to the rational S^1-equivariant stable homotopy category whose objects represent rational S^1-equivariant cohomology theories. 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.

rational homotopy theory. equivariant stable homotopy theory, Memoirs of the AMS, 1999. John Greenlees, Rational SO(3)-Equivariant Cohomology Theories, in Homotopy methods in algebraic topology (Boulder, CO, 1999), Contemp. rational equivariant homotopy theory. rational equivariant stable homotopy theory. rational stable homotopy theory. rational parameterized stable homotopy theory. Brooke Shipley, An algebraic model for rational. equivariant stable homotopy theory (pdf). David Barnes, Classifying Dihedral.

On some adjunctions in equivariant stable. In Part I we construct a complete algebraic model for the homotopy category of S 1 spectra, reminiscent of the localization theorem. Po hu, igor kriz and petr somberg. Stable homotopy of algebraic theories. The model is of homological dimension one, and simple enough to allow practical calculations; in particular we obtain a classi cation of rational S 1 -equivariant cohomology theories. In Part II we identify the algebraic counterparts of all the usual S 1 -spectra and constructions on S 1 -spectra.

**Author:**J. P. C. Greenlees

**ISBN:**0821810014

**Category:**Science & Math

**Subcategory:**Mathematics

**Language:**English

**Publisher:**Amer Mathematical Society (March 1, 1999)

**Pages:**289 pages