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L2-invariants : theory and applications to geometry and K-theory

Author: Wolfgang Lück
Publisher: Berlin : Springer, 2002.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 3, 44.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Wolfgang Lück
ISBN: 3540435662 9783540435662
OCLC Number: 248566129
Description: XV, 595 Seiten.
Contents: 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.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 3, 44.
Responsibility: Wolfgang Lück.

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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 Read more...

 
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