عنوان

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

(Number (ISBN

9783642078101

(Number (ISBN

9783662046876

Number

b399625

Title Proper

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

General Material Designation

[Book]

First Statement of Responsibility

by Wolfgang Lück.

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

2002.

Series Title

Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics,

Volume Designation

44

ISSN of Series

0071-1136 ;

Text of Note

0. Introduction -- 1. L2-Betti Numbers -- 2. Novikov-Shubin Invariants -- 3. L2-Torsion -- 4. L2-Invariants of 3-Manifolds -- 5. L2-Invariants of Symmetric Spaces -- 6. L2-Invariants for General Spaces with Group Action -- 7. Applications to Groups -- 8. The Algebra of Affiliated Operators -- 9. Middle Algebraic K-Theory and L-Theory of von Neumann Algebras -- 10. The Atiyah Conjecture -- 11. The Singer Conjecture -- 12. The Zero-in-the-Spectrum Conjecture -- 13. The Approximation Conjecture and the Determinant Conjecture -- 14. L2-Invariants and the Simplicial Volume -- 15. Survey on Other Topics Related to L2-Invariants -- 16. Solutions of the Exercises -- References -- Notation.

0

Text of Note

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.

International Standard Book Number

9783642078101

Title

Springer eBooks

K-theory.

Mathematics.

Topology.

Lück, Wolfgang.

SpringerLink (Online service)

Date of Transaction

20190307154800.0

Electronic name

[Book]

Y