Positive scalar curvature, higher rho invariants and localization algebras
Abstract
In this paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar curvature problems. The main result of the paper connects the higher index of the Dirac operator on a spin manifold with boundary to the higher rho invariant of the Dirac operator on the boundary, where the boundary is endowed with a positive scalar curvature metric. Our result extends a theorem of Piazza and Schick.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.4418
 Bibcode:
 2013arXiv1302.4418X
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras;
 46L80;
 58B34;
 53C20
 EPrint:
 33 pages, 1 figure