The Ruelle-Sullivan map for actions of ℝn
The Ruelle-Sullivan map for actions of ℝn
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ℝn 动作的 Ruelle-Sullivan 映射
DOI：
10.1007/s00208-005-0728-1
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发表时间：
2006
影响因子：
1.4
通讯作者：
I. Putnam
中科院分区：
文献类型：
--
作者：
J. Kellendonk;I. Putnam
紧致度量空间上具有不变概率测度的Cnn-作用的Ruelle Sullivan映射是空间的整数Cech上同调与Cnn的对偶的外代数之间的分次同态。我们研究了环面上的流动，以说明它检测系统的几何结构。对于行动所产生的Delone集的有限的局部复杂性，存在的规范横截和制定方面的模式等变函数导致的结果，Ruelle沙利文地图甚至是一个环同态提供的措施是遍历的。
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.