Perturbations of Dirac Operators and A KKW Type Theorem for Five Dimensional Manifolds with Boundary

TL;DR

This paper extends the Kastler-Kalau-Walze theorem to five-dimensional spin manifolds with boundary, incorporating perturbations of Dirac operators and defining lower dimensional volumes.

Contribution

It introduces a new theorem for perturbed Dirac operators on five-dimensional manifolds with boundary, expanding the understanding of geometric invariants.

Findings

Established a Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary.

Defined lower dimensional volumes for manifolds with boundary.

Connected perturbations of Dirac operators to geometric invariants.

Abstract

In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac operators in this case.