The generalized noncommutative residue and the Kastler-Kalau-Walze type theorem

2022/04/23 by Tong Wu, Yong Wang, Wu, Tong +1
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.11021

openalex publication_date 2022/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define the generalized noncommutative residue of the Dirac operator. And we give the proof of Kastler-Kalau-Walze type theorems for the generalized noncommutative residue on 4-dimensional and 6-dimensional compact manifolds with (resp.without) boundary.

Related

• The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems
• The Rescaled Dirac operator fDh and the noncommutative residue for 6-dimensional manifolds
• Twisted Dirac Operators and the noncommutative residue for manifolds with boundary II
• Twisted Dirac Operators and the Noncommutative Residue for Manifolds with Boundary
• Noncommutative Residue and Dirac operators for Manifolds with the Conformal Robertson-Walker metric