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L2-Invariants: Theory and Applications to Geometry and K-Theory

  • Wolfgang Lück

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 44)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Wolfgang Lück
    Pages 1-12
  3. Wolfgang Lück
    Pages 13-69
  4. Wolfgang Lück
    Pages 71-118
  5. Wolfgang Lück
    Pages 119-210
  6. Wolfgang Lück
    Pages 211-221
  7. Wolfgang Lück
    Pages 223-234
  8. Wolfgang Lück
    Pages 293-316
  9. Wolfgang Lück
    Pages 317-334
  10. Wolfgang Lück
    Pages 369-416
  11. Wolfgang Lück
    Pages 417-435
  12. Wolfgang Lück
    Pages 437-451
  13. Wolfgang Lück
    Pages 485-506
  14. Wolfgang Lück
    Pages 511-557
  15. Back Matter
    Pages 559-595

About this book

Introduction

In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material.

Keywords

Algebraic K-theory Algebraic topology Area K-Theory L2-Invariants Volume topology

Authors and affiliations

  • Wolfgang Lück
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04687-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07810-1
  • Online ISBN 978-3-662-04687-6
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site