Annals of Global Analysis and Geometry

, Volume 10, Issue 2, pp 103–123

Non-negative scalar curvature

  • Varghese Mathai
Article

DOI: 10.1007/BF00130915

Cite this article as:
Mathai, V. Ann Glob Anal Geom (1992) 10: 103. doi:10.1007/BF00130915

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 curvatureeta invariantsNovikov conjecturefoliations

MCS 1991

53C58G

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

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