Noncommutative Residue and sub-Dirac Operators for Foliations

Abstract

In this paper, we define lower dimensional volumes associated to sub-Dirac operators for foliations. In some cases, we compute these lower dimensional volumes. We also prove the Kastler-Kalau-Walze type theorems for foliations with or without boundary. As a corollary, we give an explanation of the gravitational action for the Robertson-Walker space $[a,b]{\times }_f{M}^3$.

32 pages. arXiv admin note: text overlap with arXiv:0907.3012

References in corpus (5)

• 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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Cited by in corpus (2)

• Dirac Operators with Torsion and the Noncommutative Residue for Manifolds with Boundary
• A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary