Rational S¹-Equivariant Stable Homotopy Theory

Erscheinungsjahr 1999
ISBN: 978-0-8218-1001-9
Verlag: American Mathematical Society

Buch, Englisch

The memoir presents a systematic study of rational S¹-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 S¹-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

The memoir presents a systematic study of rational S¹-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 S¹-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie