An equivariant Kastler-Kalau-Walze type theorem

TL;DR

This paper establishes an equivariant Kastler-Kalau-Walze type theorem for spin manifolds, including boundary cases and general dimensions, with extensions to torsion cases, advancing the understanding of geometric invariants in noncommutative geometry.

Contribution

It introduces new equivariant Kastler-Kalau-Walze theorems for spin manifolds of various dimensions, including boundary and torsion cases, expanding the theorem's applicability.

Findings

Proved the theorem for 6-dimensional boundaryless spin manifolds.

Extended the theorem to general n-dimensional manifolds.

Established the theorem with torsion effects.

Abstract

In this paper, we prove an equivariant Kastler-Kalau-Walze type theorem for spin manifolds without boundary. For $6$ dimensional spin manifolds with boundary, we also give an equivariant Kastler-Kalau-Walze type theorem. Then we generalize this theorem to the general $n$ dimensional manifold. An equivariant Kastler-Kalau-Walze type theorem with torsion is also proved.