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Birkhäuser

Homotopy Theory of C*-Algebras

  • Book
  • © 2010

Overview

Authors:
  1. Paul Arne Østvær

    1. University of Oslo, Department of Mathematics, Oslo, Norway

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  • First account of the homotopy theoretic viewpoint of C*-algebras encoded in the notion of a C*-space
  • Unifies two separate mathematical topics
  • Opens up for a whole host of new research problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Frontiers in Mathematics (FM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction

    • Paul Arne Østvær
    Pages 1-5

  3. Preliminaries

    • Paul Arne Østvær
    Pages 7-24

  4. Unstable C*-homotopy theory

    • Paul Arne Østvær
    Pages 25-67

  5. Stable C*-homotopy theory

    • Paul Arne Østvær
    Pages 69-105

  6. Invariants

    • Paul Arne Østvær
    Pages 107-129

  7. The slice filtration

    • Paul Arne Østvær
    Pages 131-134

  8. Back Matter

    Pages 135-139
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Keywords

About this book

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.

Authors and Affiliations

  • University of Oslo, Department of Mathematics, Oslo, Norway

    Paul Arne Østvær

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