Annals of Global Analysis and Geometry

, Volume 10, Issue 2, pp 103–123

Non-negative scalar curvature

  • Varghese Mathai
Article

Abstract

We study topological obstructions to the existence of Riemannian metrics of non-negative scalar curvature on almost spin manifolds using the Dirac operator, the Bochner technique, C* algebras and von Neumann algebras. We also derive some obstructions in terms of the eta invariants of Atiyah, Patodi and Singer. Next, we prove vanishing theorems for the Atiyah-Milnor genus. Finally, we derive obstructions to the existence of metrics of non-negative scalar curvature along the leaves of a leafwise non-amenable foliation on a spin manifold.

Key words

Scalar curvature eta invariants Novikov conjecture foliations 

MCS 1991

53C 58G 

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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Varghese Mathai
    • 1
  1. 1.Department of Pure MathematicsThe University of AdelaideSouth Australia

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