Connes-Landi Deformation of Spectral Triples

Abstract

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic $K$-theoretic invariants independent of the deformation parameter.

19 pages

References in corpus (5)

• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Metrics on states from actions of compact groups
• A Local Index Formula for the Quantum Sphere
• theta-deformations as compact quantum metric spaces
• Group C*-algebras, metrics and an operator theoretic inequality

Cited by in corpus (11)

• K-homology class of the Dirac operator on a compact quantum group
• Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds
• Gauge theory on noncommutative Riemannian principal bundles
• A reconstruction theorem for Connes-Landi deformations of commutative spectral triples
• Nonclassical spectral asymptotics and Dixmier traces: From circles to contact manifolds
• Smooth crossed products of Rieffel's deformations
• Index pairings for ${\mathbb{R}}^n$-actions and Rieffel deformations
• Deformation of algebras associated with group cocycles
• KK-fibrations arising from Rieffel deformations
• Poincare duality for Cuntz-Pimsner algebras of bimodules
• Monodromy of the Gauss-Manin connection for deformation by group cocycles