Lower dimensional volumes and the Kastler-Kalau-Walze type theorem for Manifolds with Boundary

Abstract

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\mathrm{Vol}}^{(2,2)}$ for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case.

References in corpus (4)

• Differential Forms and the Wodzicki Residue for Manifolds with Boundary
• Gravity and the Noncommutative Residue for Manifolds with Boundary
• Differential Forms and the Noncommutative Residue for Manifolds with Boundary in the Non-product Case
• Noncommutative geometry and lower dimensional volumes in Riemannian geometry

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• Noncommutative Residue and sub-Dirac Operators for Foliations
• A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator
• Sub-signature Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary
• The spectral torsion for the Connes type operator
• The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary
• Spectral forms and de-Rham Hodge operator
• The Spectral Einstein functional and Kastler-Kalau-Walze type theorems
• Nonminimal De Rham-Hodge Operators and Non-commutative Residue
• Equivariant Bismut Laplacian and spectral Einstein functional
• Dirac-Witten Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary