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On the Noncommutative Geometry of Tilings

  • Antoine Julien
  • Johannes Kellendonk
  • Jean Savinien
Part of the Progress in Mathematics book series (PM, volume 309)

Abstract

We discuss constructions of spectral triples for spaces which are related to subshifts or aperiodic tilings. These spectral triples give rise to distance functions, zeta functions, Laplace operators and K-homology classes. We investigate these objects, and relate their properties to standard notions in tiling theory.

Keywords

Spectral triples subshifts tilings 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Antoine Julien
    • 1
  • Johannes Kellendonk
    • 2
  • Jean Savinien
    • 3
  1. 1.NTNUTrondheimNorway
  2. 2.CNRS, UMR 5208 Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne cedexFrance
  3. 3.Institut Elie Cartan de LorraineUniversité de LorraineMetzFrance

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