Noncommutative geometry and lower dimensional volumes in Riemannian geometry

DOI10.1007/s11005-007-0199-2zbMath1136.58017arXiv0707.4201OpenAlexW3102276091WikidataQ115381915 ScholiaQ115381915MaRDI QIDQ2476619

Raphaël Ponge

Publication date: 12 March 2008

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.4201

zbMATH Keywords

noncommutative geometrypseudodifferential operatorslocal Riemannian geometry

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Local Riemannian geometry (53B20) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (23)

ON THE SINGULARITIES OF THE ZETA AND ETA FUNCTIONS OF AN ELLIPTIC OPERATOR ⋮ Dirac-Witten operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary ⋮ The general Kastler-Kalau-Walze type theorems about Witten deformation ⋮ The Kastler-Kalau-Walze type theorem about Witten deformation for manifolds with boundary ⋮ A Kastler-Kalau-Walze type theorem for 7-dimensional spin manifolds with boundary about Dirac operators with torsion ⋮ The operator \(\sqrt{-1}\widehat{c}(V)(d+\delta)\) and the Kastler-Kalau-Walze type theorems ⋮ The Kastler-Kalau-Walze type theorems for the perturbation of the de Rham Hodge operator ⋮ A Kastler-Kalau-Walze type theorem for the \(J\)-twist \(D_J\) of the Dirac operator ⋮ The J-twist DJ of the Dirac operator and the Kastler–Kalau–Walze type theorem for six-dimensional manifolds with boundary ⋮ Wodzicki residue for operators on manifolds with cylindrical ends ⋮ An equivariant Kastler–Kalau–Walze type theorem ⋮ A Kastler-Kalau-Walze type theorem for 7-dimensional manifolds with boundary ⋮ General Kastler–Kalau–Walze type theorems for manifolds with boundary II ⋮ Connes’s trace theorem for curved noncommutative tori: Application to scalar curvature ⋮ The noncommutative residue about Witten deformation ⋮ Noncommutative residue and sub-Dirac operators for foliations ⋮ A note on the Einstein-Hilbert action and Dirac operators on \({\mathbb{R}^n}\) ⋮ Modified Novikov operators and the Kastler-Kalau-Walze-type theorem for manifolds with boundary ⋮ A Kastler-Kalau-Walze Type Theorem for 7-dimensional Manifolds with Boundary about Witten deformation ⋮ Sub-signature operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary ⋮ The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary ⋮ A Kastler–Kalau–Walze type theorem for five-dimensional manifolds with boundary ⋮ Nonminimal operators and non-commutative residue

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gravity coupled with matter and the foundation of non-commutative geometry
• Local invariants of spectral asymmetry
• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• The action functional in non-commutative geometry
• Residue traces for certain algebras of Fourier integral operators
• The Dirac operator and gravitation
• The spectral action principle
• Gravity, non-commutative geometry and the Wodzicki residue
• The local index formula in noncommutative geometry
• A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
• Gravity and the standard model with neutrino mixing
• An asymptotic expansion for the heat equation
• On the heat equation and the index theorem
• Leading terms in the heat invariants for the Laplacians of the De Rham signature, and spin complexes.

This page was built for publication: Noncommutative geometry and lower dimensional volumes in Riemannian geometry