Spectral triples and the geometry of fractals

DOI10.4171/JNCG/91zbMath1244.28010arXiv1002.3081WikidataQ59123176 ScholiaQ59123176MaRDI QIDQ426732

Erik Christensen, Cristina Ivan, Elmar Schrohe

Publication date: 12 June 2012

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

Full work available at URL: https://arxiv.org/abs/1002.3081

zbMATH Keywords

Sierpiński gasketspectral tripleK-homologynon commutative geometry

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Geodesics in global differential geometry (53C22) Fractals (28A80) Noncommutative geometry (à la Connes) (58B34)

Related Items (15)

Noncommutative potential theory: a survey ⋮ Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality ⋮ A noncommutative Sierpinski gasket ⋮ Fractality in cosmic topology models with spectral action gravity ⋮ Wavelets and spectral triples for fractal representations of Cuntz algebras ⋮ Isometry groups of inductive limits of metric spectral triples and Gromov–Hausdorff convergence ⋮ From Monge to Higgs: a survey of distance computations in noncommutative geometry ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ Examples of infinite direct sums of spectral triples ⋮ Spectral triples for the Sierpinski gasket ⋮ Spectral triples and wavelets for higher-rank graphs ⋮ A spectral triple for a solenoid based on the Sierpinski gasket ⋮ Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves ⋮ Bell polynomials and Brownian bridge in spectral gravity models on multifractal Robertson-Walker cosmologies ⋮ Asymptotic and exact expansions of heat traces

Cites Work

• Extensions of \(C^*\)-algebras and \(K\)-homology
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