Author | Lรผck, Wolfgang. author |
---|---|

Title | L2-Invariants: Theory and Applications to Geometry and K-Theory [electronic resource] / by Wolfgang Lรผck |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002 |

Connect to | http://dx.doi.org/10.1007/978-3-662-04687-6 |

Descript | XV, 595 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
K-theory
Geometry
Topology
Algebraic topology
Mathematics
Algebraic Topology
Geometry
K-Theory
Topology