Open Access
Translator Disclaimer
January, 2001 Coarse Obstructions to Positive Scalar Curvature in Noncompact Arithmetic Manifolds
Stanley S. Chang
J. Differential Geom. 57(1): 1-21 (January, 2001). DOI: 10.4310/jdg/1090348087


Block and Weinberger show that an arithmetic manifold can be endowed with a positive scalar curvature metric if and only if its ℚ-rank exceeds 2. We show in this article that these metrics are never in the same coarse class as the natural metric inherited from the base Lie group. Furthering the coarse C*-algebraic methods of Roe, we find a nonzero Dirac obstruction in the K-theory of a particular operator algebra which encodes information about the quasi-isometry type of the manifold as well as its local geometry.


Download Citation

Stanley S. Chang. "Coarse Obstructions to Positive Scalar Curvature in Noncompact Arithmetic Manifolds." J. Differential Geom. 57 (1) 1 - 21, January, 2001.


Published: January, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1067.53024
MathSciNet: MR1871489
Digital Object Identifier: 10.4310/jdg/1090348087

Rights: Copyright © 2001 Lehigh University


Vol.57 • No. 1 • January, 2001
Back to Top