Rational $S^1$-Equivariant Stable Homotopy Theory
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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. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of $S^1$-equivariant $K$-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.
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