# Twisted Dirac Operators and the noncommutative residue for manifolds with boundary II

## TL;DR

This paper proves new Kastler-Kalau-Walze type theorems for twisted Dirac and signature operators on six-dimensional manifolds with boundary, expanding the understanding of noncommutative residues in geometric analysis.

## Contribution

It introduces two new Kastler-Kalau-Walze type theorems for twisted Dirac and signature operators on manifolds with boundary, considering non-unitary connections.

## Key findings

- Established Kastler-Kalau-Walze type theorems for twisted operators
- Extended residue formulas to six-dimensional manifolds with boundary
- Analyzed effects of non-unitary connections on residues

## Abstract

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.