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

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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-in...

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Bibliographic Details
Main Author: Lück, Wolfgang
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ; 44.
Subjects:
Mathematics.
K-theory.
Topology.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction
  • L2-Betti Numbers
  • Novikov-Shubin Invariants
  • L2-Torsion
  • L2-Invariants of 3-Manifolds
  • L2-Invariants of Symmetric Spaces
  • L2-Invariants for General Spaces with Group Action
  • Applications to Groups
  • The Algebra of Affiliated Operators
  • Middle Algebraic K-Theory and L-Theory of von Neumann Algebras
  • The Atiyah Conjecture
  • The Singer Conjecture
  • The Zero-in-the-Spectrum Conjecture
  • The Approximation Conjecture and the Determinant Conjecture
  • L2-Invariants and the Simplicial Volume
  • Survey on Other Topics Related to L2-Invariants
  • Solutions of the Exercises
  • References
  • Notation
  • Index.