Spectral triples for the variants of the Sierpiński gasket

DOI10.4171/JFG/75zbMath1428.28010arXiv1709.00755MaRDI QIDQ2327715

Andrea Arauza Rivera

Publication date: 15 October 2019

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.00755

zbMATH Keywords

non-commutative geometryHausdorff measurefractal setsspectral dimensionSierpiński gasketDixmier tracespectral triplesnon-commutative measureanalysis on fractalsHanoi attractorfractals built on curvesgeodesics on fractalsnon-commutative metrics

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Noncommutative differential geometry (46L87) Integration on manifolds; measures on manifolds (58C35) Noncommutative measure and integration (46L51) Geodesics in global differential geometry (53C22) Noncommutative geometry in quantum theory (81R60) Fractals (28A80) Noncommutative geometry (à la Connes) (58B34) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (3)

Unnamed Item ⋮ A spectral triple for a solenoid based on the Sierpinski gasket ⋮ Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

Cites Work

• Singular traces. Theory and applications
• Metrics on states from actions of compact groups
• Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions
• Dimensions and singular traces for spectral triples, with applications to fractals
• Completely symmetric resistance forms on the stretched Sierpiński gasket
• Metrics on state spaces
• Spectral triples for the Sierpinski gasket
• Dirac operators and geodesic metric on the harmonic Sierpiński gasket and other fractal sets
• Weyl asymptotics for Hanoi attractors
• Dirac operators and spectral triples for some fractal sets built on curves
• Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate
• Analysis and Geometry of the Measurable Riemannian Structure on the Sierpiński Gasket
• Energy and Laplacian on Hanoi-type fractal quantum graphs
• The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
• Compact metric spaces, Fredholm modules, and hyperfiniteness
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