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" L2-Invariants: Theory and Applications to Geometry and K-Theory "
by Wolfgang Lück.
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BL
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| Record Number
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570406
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b399625
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| Main Entry
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Lück, Wolfgang.
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| Title & Author
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L2-Invariants: Theory and Applications to Geometry and K-Theory\ by Wolfgang Lück.
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| Publication Statement
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Berlin, Heidelberg :: Springer Berlin Heidelberg :: Imprint: Springer,, 2002.
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| Series Statement
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Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics,; 44
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| ISBN
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9783662046876
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: 9783642078101
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| Contents
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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.
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| Abstract
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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-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.
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Mathematics.
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K-theory.
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Topology.
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SpringerLink (Online service)
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