Homotopy Theory of C*-Algebras

• Main Author: <U+00d8>stvr̆, Paul Arne. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Springer Basel, 2010.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Functional analysis.; Algebraic topology.; Algebraic Topology.; Functional Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0346-0565-6

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 suitab...

Table of Contents:

• 1 Introduction
• 2 Preliminaries
• 2.1 C*-spaces
• 2.2 G <U+0013> 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.