Johannes Kellendonk, Ian F. Putnam
The Ruelle-Sullivan map for actions of $R^n$
(299K, pdf)
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.