Overview

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.

Full Product Details

Author:   Wolfgang Lück
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Volume:   44
Dimensions:   Width: 15.50cm , Height: 3.30cm , Length: 23.50cm
Weight:   2.290kg
ISBN:  

9783540435662

ISBN 10:   3540435662
Pages:   595
Publication Date:   06 August 2002
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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. ... Luck'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)

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. ! Luck'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)

From the reviews: <p> The book under review represents a fundamental monograph on the theory of L2-invariants. a ] To a great extent, it is self-contained. a ] The book is very clearly written, it contains many examples and we can find exercises at the end of each chapter. a ] At many places in the book, the reader will find hints for further research. a ] The book will be of great interest to specialists but it can also be strongly recommended for postgraduate students. (EMS Newsletter, March, 2005) <p> L2-invariants were introduced into topology by Atiyah in 1976 a ] . Since then, the theory has been developed successfully by many researchers, among them the author of this monograph a ] . This book is an excellent survey of many up-to-date results a ] . It could be used as a very good introduction to the subject of L2-invariants a ] usable either for self-study or as a text for a graduate course. a ] LA1/4cka (TM)s book will become the primary reference about L2-variants for the foreseeable future. (Thomas Schick, Mathematical Reviews, 2003 m) <p> L2-invariants were introduced into topology by Atiyah in the 1970a (TM)s a ] . The present book is the first substantial monograph on this topic. a ] This is an impressive account of much of what is presently known about these invariants a ] . 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)

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