Continuity for the spectral propinquity of the Dirac operators associated with an analytic path of Riemannian metrics

2025/04/16 by Carla Farsi, Frédéric Latrémolière, Farsi, Carla +1
Mathematics · #Geometric Analysis and Curvature Flows #Advanced Operator Algebra Research #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2504.11715

Abstract

We prove that a polynomial path of Riemannian metrics on a closed spin manifold induces a continuous field in the spectral propinquity of metric spectral triples.

Citations

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• The Dual Gromov-Hausdorff Propinquity
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• Dirac operator on spinors and diffeomorphisms
• The spinorial energy functional on surfaces
• Natural connections on the bundle of Riemannian metrics
• The uniqueness of the spectral flow on spaces of unbounded self--adjoint Fredholm operators
• ?-Deformations as Compact Quantum Metric Spaces
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Related

• Collapse in Noncommutative Geometry and Spectral Continuity
• The Dirac operator under collapse to a smooth limit space
• The spectrum of basic Dirac operators
• Dirac operator associated to a quantum metric
• Equivariant Spectral Flow for Families of Dirac-type Operators