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© 2010

Homotopy Theory of C*-Algebras

Benefits

  • 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

Book

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-v
  2. Paul Arne Østvær
    Pages 1-5
  3. Paul Arne Østvær
    Pages 7-24
  4. Paul Arne Østvær
    Pages 25-67
  5. Paul Arne Østvær
    Pages 69-105
  6. Paul Arne Østvær
    Pages 107-129
  7. Paul Arne Østvær
    Pages 131-134
  8. Back Matter
    Pages 135-139

About this book

Introduction

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.

Keywords

Algebraic topology Brown representability Cohomology Homotopy K-theory homology homotopy theory

Authors and affiliations

  1. 1.University of OsloDepartment of MathematicsOsloNorway

Bibliographic information