L2-Invariants of Symmetric Spaces

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


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.


Riemannian Manifold Symmetric Space Sectional Curvature Universal Covering Complete Riemannian Manifold 
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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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