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L2-Invariants of Symmetric Spaces

  • Wolfgang Lück
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 44)

Abstract

In this chapter we state the values of the L 2-Betti numbers, the NovikovShubin invariants and the L 2-torsion for universal coverings of closed locally symmetric spaces. We give a brief survey about locally symmetric and symmetric spaces in Section 5.1 and state the values in Section 5.2 and 5.3. These computations will give evidence for various general conjectures about L 2-invariants such as Conjecture 2.82 about the positivity and rationality of Novikov-Shubin invariants, the Strong Atiyah Conjecture 10.2, the Singer Conjecture 11.1, Conjecture 11.3 about the parity of the L 2-torsion of the universal covering of an aspherical closed manifold and the zero-in-the-spectrum Conjecture 12.1.

Keywords

Riemannian Manifold Symmetric Space Sectional Curvature Universal Covering Complete Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Wolfgang Lück
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany

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