The general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for odd dimensional manifold with boundary

TL;DR

This paper proves generalized versions of the Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for odd-dimensional compact manifolds with boundary, extending their applicability.

Contribution

It provides the first proof of these theorems in the context of odd-dimensional manifolds with boundary, broadening their theoretical scope.

Findings

Established the generalized Kastler-Kalau-Walze theorem for odd-dimensional manifolds with boundary.

Proved the Dabrowski-Sitarz-Zalecki theorem in the same setting.

Extended the applicability of these theorems to new geometric contexts.

Abstract

In this paper, we give the proof of the general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem on odd dimensional compact manifolds with boundary.