• Corpus ID: 244908967

On finitely summable Fredholm modules from Smale spaces

  title={On finitely summable Fredholm modules from Smale spaces},
  author={D. M. Gerontogiannis},
We prove that all K-homology classes of the stable (and unstable) Ruelle algebra of a Smale space have explicit Fredholm module representatives that are finitely summable on the same smooth subalgebra and with the same degree of summability. The smooth subalgebra is induced by a metric on the underlying Smale space groupoid and fine transversality relations between stable and unstable sets. The degree of summability is related to the fractal dimension of the Smale space. Further, the Fredholm… 


Compact metric spaces, Fredholm modules, and hyperfiniteness
  • A. Connes
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1989
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