SOFIC GROUPS AND DYNAMICAL SYSTEMS
SOFIC GROUPS AND DYNAMICAL SYSTEMS
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发表时间：
2000
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通讯作者：
B. Weiss
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作者：
B. Weiss
摘要Sofic群是由M. Gromov是顺从群和剩余有限群的一个普通推广。我们讨论了这个新的类，特别是它的关系，一个老问题的拓扑动力学的W。Gottschalk关于超接群拓扑动力学的基本研究对象是一对（X;G），其中X是拓扑空间，G是群，以及从G到X的同胚群的同态。在经典动力学中，G = R，R的作用量是由一些微分方程组的解定义的。我们在这里感兴趣的是可数群G，对于可数群G，在紧空间f 1;2; AG G =<$1上定义了一个非常自然的作用，称为移位ae，由下式给出：
SUMMARY. Sofic groups were first defined by M. Gromov as a common generalization of amenable groups and residually finite groups. We discuss this new class and especially its relationship to an old problem in topological dynamics of W. Gottschalk on surjunctive groups. The basic objects of study in topological dynamics are a pair (X;G) with X a topological space and G a group, together with a homomorphism from G into the group of homeomorphisms of X. In classical dynamics G = R and the action of R is defined by the solutions of some system of dierential equations. Our interest here will be in countable groups G, for which there is a very natural action defined on the compact space f1;2;¢¢¢ag G = › called the shift ae given by: