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Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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

Authors: Lück, Wolfgang

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  • ISBN 978-3-662-04687-6
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Hardcover 129,99 €
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  • ISBN 978-3-540-43566-2
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Softcover 89,99 €
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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.

Reviews

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)


Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook 74,89 €
price for China (P.R.) (gross)
  • ISBN 978-3-662-04687-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 129,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-540-43566-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover 89,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-642-07810-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
L2-Invariants: Theory and Applications to Geometry and K-Theory
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
44
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04687-6
DOI
10.1007/978-3-662-04687-6
Hardcover ISBN
978-3-540-43566-2
Softcover ISBN
978-3-642-07810-1
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XV, 595
Topics