Mathematische Annalen

, Volume 334, Issue 3, pp 693–711 | Cite as

The Ruelle-Sullivan map for actions of ℝ n

  • Johannes KellendonkEmail author
  • Ian F. Putnam


The Ruelle Sullivan map for an ℝ n -action on a compact metric space with invariant probability measure is a graded homomorphism between the integer Cech cohomology of the space and the exterior algebra of the dual of ℝ n . We investigate flows on tori to illuminate that it detects geometrical structure of the system. For actions arising from Delone sets of finite local complexity, the existence of canonical transversals and a formulation in terms of pattern equivariant functions lead to the result that the Ruelle Sullivan map is even a ring homomorphism provided the measure is ergodic.


Probability Measure Geometrical Structure Equivariant Function Ring Homomorphism Invariant Probability Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institute Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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