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The Ruelle-Sullivan map for actions of ℝn

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Abstract

The Ruelle Sullivan map for an ℝn-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 ℝn. 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.

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Authors and Affiliations

  1. Institute Camille Jordan, Université Claude Bernard Lyon 1, 69622, Villeurbanne

    Johannes Kellendonk

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, B. C. V8W 3P4, Canada

    Ian F. Putnam

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  1. Johannes Kellendonk
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  2. Ian F. Putnam
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Correspondence to Johannes Kellendonk.

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Kellendonk, J., Putnam, I. The Ruelle-Sullivan map for actions of ℝn . Math. Ann. 334, 693–711 (2006). https://doi.org/10.1007/s00208-005-0728-1

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  • DOI: https://doi.org/10.1007/s00208-005-0728-1

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