Orbit equivalence, flow equivalence and ordered cohomology
Orbit equivalence, flow equivalence and ordered cohomology
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轨道等效、流等效和有序上同调
DOI：
10.1007/bf02761039
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发表时间：
1996
影响因子：
1
通讯作者：
D. Handelman
中科院分区：
文献类型：
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作者：
Mike Boyle;D. Handelman
摘要借鉴了Giordano Putnam和Skau关于极小同胚的最新研究成果，利用有序第一上同调群研究了零维可度量紧化Hausdorff空间的自同胚。我们证明了系统的流动等价类似于代数间的Morita等价，这反映在有序上同群上。证明了有限型不可约位移间流动等价的有序上同群是完全不变量；由此可见，轨道等价意味着这类系统的流动等价。上同调群是C*-代数交叉积的（预序）Grothendieck群，我们可以从动力学性质上判断该预序何时为有序。
We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces by means of the ordered first cohomology group, particularly in the light of the recent work of Giordano Putnam, and Skau on minimal homeomorphisms. We show that flow equivalence of systems is analogous to Morita equivalence between algebras, and this is reflected in the ordered cohomology group. We show that the ordered cohomology group is a complete invariant for flow equivalence between irreducible shifts of finite type; it follows that orbit equivalence implies flow equivalence for this class of systems. The cohomology group is the (pre-ordered) Grothendieck group of the C*-algebra crossed product, and we can decide when the pre-ordering is an ordering, in terms of dynamical properties.
关于部分定义的代数结构的空间分类
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
Toshiaki;ADACHI;松木敏彦;Dai Tamaki;Toshiaki ADACHI;T.Matsuki;Dai Tamaki
通讯作者：
Dai Tamaki