Asian Journal of Mathematics
Volume 26 (2022)
Higher rho invariant and delocalized eta invariant at infinity
Pages: 257 – 288
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.
Dirac operator, higher index, higher rho invariant at infinity, delocalized eta invariant at infinity, uniform positive scalar curvature, polynomial growth conjugacy class
2010 Mathematics Subject Classification
19K56, 58B34, 58J20
The first-named author is partially supported by NSFC 11420101001.
The second-named author is partially supported by NSFC 11901374.
The third-named author is partially supported by the Shanghai Rising-Star Program grant 19QA1403200, and by NSFC 11801178.
The fourth-named author is partially supported by NSF 1700021, NSF 1564398, and by the Simons Fellows Program.
Received 24 August 2021
Accepted 3 December 2021
Published 6 March 2023