Higher rho invariant and delocalized eta invariant at infinity

TL;DR

This paper introduces new secondary invariants for Dirac operators on non-compact manifolds with positive scalar curvature outside a compact set, establishing a higher index theorem and analyzing manifolds with corners.

Contribution

It develops novel secondary invariants for Dirac operators and proves a higher index theorem applicable to manifolds with corners and positive scalar curvature.

Findings

New secondary invariants for Dirac operators introduced

Higher index theorem established for manifolds with positive scalar curvature

Analysis of secondary invariants on manifolds with corners

Abstract

In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a higher index theorem for the Dirac operators. We apply our theory to study the secondary invariants for a manifold with corner with positive scalar curvature metric on each boundary face.