Asian Journal of Mathematics

Volume 26 (2022)

Number 2

Higher rho invariant and delocalized eta invariant at infinity

Pages: 257 – 288



Xiaoman Chen (School of Mathematical Sciences, Fudan University)

Hongzhi Liu (School of Mathematics, Shanghai University of Finance and Economics)

Hang Wang (School of Mathematical Sciences, East China Normal University)

Guoliang Yu (Department of Mathematics, Texas A&M University)


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