Equivariant Twisted Bismut Laplacian with Torsion and KKW type theorems

TL;DR

This paper computes the noncommutative residue density for an equivariant twisted Bismut Laplacian with torsion and establishes related Kastler-Kalau-Walze type theorems on compact manifolds, including those with boundary.

Contribution

It provides explicit residue computations and extends Kastler-Kalau-Walze theorems to equivariant twisted Laplacians with torsion on manifolds with boundary.

Findings

Explicit noncommutative residue density formulas.

Proof of equivariant twisted Kastler-Kalau-Walze theorems with torsion.

Extension of results to manifolds with boundary.

Abstract

This paper aims to provide an explicit computation of the noncommutative residue density associated with equivariant twisted Bismut Laplacian with torsion on compact manifolds with (or without) boundary. We prove the equivariant twisted Kastler-Kalau-Walze type theorems with torsion on compact manifolds with boundary.