05-56 Johannes Kellendonk, Ian F. Putnam

The Ruelle-Sullivan map for actions of $R^n$ (299K, pdf) Feb 8, 05

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Abstract. 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.

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