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

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.

References in corpus (4)

• Differential Forms and the Wodzicki Residue for Manifolds with Boundary
• Gravity and the Noncommutative Residue for Manifolds with Boundary
• Chiral Asymmetry and the Spectral Action
• Noncommutative Residue and sub-Dirac Operators for Foliations

Cited by in corpus (7)

• Dirac operators with torsion, spectral Einstein functionals and the noncommutative residue
• A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary
• The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor
• Sub-signature Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary
• The spectral torsion for the Connes type operator
• Spectral forms and de-Rham Hodge operator
• A Kastler-Kalau-Walze Type Theorem for 7-dimensional Manifolds with Boundary about Witten deformation