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L2-Invariants: Theory and Applications to Geometry and K-Theory / by Wolfgang Lück
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 44)
Edition | 1st ed. 2002. |
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Publisher | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Year | 2002 |
Language | English |
Size | XV, 595 p : online resource |
Authors | *Lück, Wolfgang author SpringerLink (Online service) |
Subjects | LCSH:Algebraic topology LCSH:Geometry LCSH:K-theory LCSH:Topology FREE:Algebraic Topology FREE:Geometry FREE:K-Theory FREE:Topology |
Notes | 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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-04687-6 |
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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783662046876 |
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EB00231512 |
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Material Type | E-Book |
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Classification | LCC:QA612-612.8 DC23:514.2 |
ID | 4000110632 |
ISBN | 9783662046876 |
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