© 2002

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


  • A comprehensive introduction to the field of L2-Invariants

  • Presents the most recent results and developments

  • Chapters are kept as independent of one other as possible

  • Each chapter includes exercises; hints to their solution are given

  • Contains an extensive index

  • The book will become a standard reference work in the field of L2-invariants


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


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.


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

Authors and affiliations

  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany

Bibliographic information

  • Book Title L2-Invariants: Theory and Applications to Geometry and K-Theory
  • Authors Wolfgang Lück
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-43566-2
  • Softcover ISBN 978-3-642-07810-1
  • eBook ISBN 978-3-662-04687-6
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages XV, 595
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Topology
  • Buy this book on publisher's site


From the reviews:

"The book under review represents a fundamental monograph on the theory of L2-invariants. … To a great extent, it is self-contained. … The book is very clearly written, it contains many examples and we can find exercises at the end of each chapter. … At many places in the book, the reader will find hints for further research. … The book will be of great interest to specialists but it can also be strongly recommended for postgraduate students." (EMS Newsletter, March, 2005)

"L2-invariants were introduced into topology by Atiyah in 1976 … . Since then, the theory has been developed successfully by many researchers, among them the author of this monograph … . This book is an excellent survey of many up-to-date results … . It could be used as a very good introduction to the subject of L2-invariants … usable either for self-study or as a text for a graduate course. … Lück’s book will become the primary reference about L2-variants for the foreseeable future." (Thomas Schick, Mathematical Reviews, 2003 m)

"L2-invariants were introduced into topology by Atiyah in the 1970’s … . The present book is the first substantial monograph on this topic. … This is an impressive account of much of what is presently known about these invariants … . It combines features of a text and a reference work; to a considerable degree the chapters can be read independently, and there are numerous nontrivial exercises, with nearly 50 pages of detailed hints at the end." (Jonathan A. Hillman, Zentralblatt MATH, Vol. 1009, 2003)