Paul Arne Østvær

Homotopy Theory of C*-Algebras

• Broschiertes Buch

Produktbeschreibung

Homotopy theory and C_ algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C_-algebras. One basic idea of the setup is to merge C_-algebras and spaces studied in algebraic topology into one category comprising C_-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C_-spaces such as homology and cohomology theories, K-theory and zeta-functions.The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C_-algebras, homotopy theory and applications.

Produktdetails

• Frontiers in Mathematics
• Verlag: Birkhäuser / Springer Basel / Springer, Basel
• Artikelnr. des Verlages: 12811069, 978-3-0346-0564-9
• 2010
• Seitenzahl: 148
• Erscheinungstermin: 10. September 2010
• Englisch
• Abmessung: 240mm x 168mm x 8mm
• Gewicht: 291g
• ISBN-13: 9783034605649
• ISBN-10: 3034605641
• Artikelnr.: 29380372

Inhaltsangabe

1 Introduction.- 2 Preliminaries.- 2.1 C*-spaces.- 2.2 G - C*-spaces.- 2.3 Model categories.- 3 Unstable C*-homotopy theory.- 3.1 Pointwise model structures.- 3.2 Exact model structures.- 3.3 Matrix invariant model structures.- 3.4 Homotopy invariant model structures.- 3.5 Pointed model structures.- 3.6 Base change.- 4 Stable C*-homotopy theory.- 4.1 C*-spectra.- 4.2 Bispectra.- 4.3 Triangulated structure.- 4.4 Brown representability.- 4.5 C*-symmetric spectra.- 4.6 C*-functors.- 5 Invariants.- 5.1 Cohomology and homology theories.- 5.2 KK-theory and the Eilenberg-MacLane spectrum.- 5.3 HL-theory and the Eilenberg-MacLane .-5.4 The Chern-Connes-Karoubi character.- 5.5 K-theory of C*-algebras.- 5.6 Zeta functions.- 6 The slice filtration.- References.- Index.