离散群的欧拉示性数与Yuzvinskii熵的加法公式
The Euler characteristic of discrete groups and Yuzvinskii's entropy addition formula
摘要：
拓扑熵的概念最初是为单个作用量定义的。后来，它被Kieffer推广到任意离散顺从群。最近Friedland定义了任意离散群作用的拓扑熵。Lind、Schmidt和Ward将Yuzvinskii的加法公式从单作用推广到阿贝尔群作用。Ward和Zhang的一个结果表明，在可处理的情况下，这种扩展是可能的。本文证明了加法公式不能推广到具有非零欧拉特征的有限型群，如自由群或曲面群。
英文摘要：
The notion of topological entropy is originally defined for a single action. Later it was extended by Kieffer for arbitrary discrete amenable groups. Recently Friedland defined topological entropy for any discrete group actions amenable or not. Lind, Schmidt and Ward extended Yuzvinskii's addition formula from single action to abelian group actions. A result of Ward and Zhang suggests that such extension might be possible in the amenable case. In this paper we prove that the addition formula can not be extended for groups of finite type with nonzero Euler-characteristcs e.g. for free groups or surface groups.
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