Positive scalar curvature, higher rho invariants and localization algebras

By Zhizhang Xie, Guoliang Yu. 2013

76 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bfa8673cff4fadca98479be8f694812c5d001dca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Thomas Schick
2. P. Piazza

In Mathematical Physics

1. P. Piazza
2. Thomas Schick
3. Guoliang Yu
4. Zhizhang Xie
5. N. Higson

In Statistical and Nonlinear Physics

1. Thomas Schick
2. P. Piazza

Citations in the corpus

• Rho‐classes, index theory and Stolz’ positive scalar curvature sequence (2012, methodology): “After the first publication of the present paper in the arXiv, Xie and Yu, in the preprint [45], treated the problem with a different method.”