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math.OAMay 1, 2020
2
citations (OpenAlex)
authors
  • Valeriano Aiello
  • Daniele Guido
  • Tommaso Isola
institutions
  • University of Bern
  • University of Rome Tor Vergata
arXiv abstractPDF
paper

A Spectral Triple for a Solenoid Based on the Sierpinski Gasket

arXiv:2005.14225 · doi:10.3842/SIGMA.2021.020

Abstract

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

References in corpus (12)

  • The quantum structure of spacetime at the Planck scale and quantum fields
  • Metrics on states from actions of compact groups
  • Dimensions and singular traces for spectral triples, with applications to fractals
  • Dynamical Systems on Spectral Metric Spaces
  • Spectral triples for the Sierpinski Gasket
  • Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets
  • Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket
  • Spectral triples for noncommutative solenoidal spaces from self-coverings
  • Dimensions and spectral triples for fractals in R^N
  • Noncommutative Riemann integration and and Novikov-Shubin invariants for open manifolds
  • A semicontinuous trace for almost local operators on an open manifold
  • A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L^2-Betti numbers

Cited by in corpus (1)

  • Spectral triples on irreversible C∗-dynamical systems
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