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

Wolfgang Lück

596 pages, parution le 14/08/2002

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Résumé

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.

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.

L'auteur - Wolfgang Lück

University of Münster, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Wolfgang Lück
Parution	14/08/2002
Nb. de pages	596
Format	16 x 24
Couverture	Relié
Poids	1035g
Intérieur	Noir et Blanc
EAN13	9783540435662