Dirac Operators with Torsion and the Noncommutative Residue for Manifolds with Boundary

TL;DR

This paper extends the Kastler-Kalau-Walze theorem to Dirac operators with torsion on manifolds with boundary, providing operator-theoretic insights into gravitational actions and exploring complex manifolds with nonminimal operators.

Contribution

It introduces new versions of the Kastler-Kalau-Walze theorem for Dirac operators with torsion and nonminimal operators on manifolds with boundary, with applications to gravitational action.

Findings

Established Kastler-Kalau-Walze theorem for Dirac operators with torsion

Provided operator-theoretic explanations for gravitational action in 4D

Extended results to complex manifolds with nonminimal operators

Abstract

In this paper, we get the Kastler-Kalau-Walze theorem associated to Dirac operators with torsion on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of 4-dimensional compact manifolds with flat boundary. Furthermore, we get the Kastler-Kalau-Walze type theorem for four dimensional complex manifolds associated with nonminimal operators.