调节子、熵与无穷行列式
Regulators, entropy and infinite determinants
摘要：
在本说明中，我们描述的情况下，值的$K$理论调节器地图上的拓扑循环相等熵的拓扑行动由一组$Γ$评估。这些熵也可以用$Γ$的冯诺依曼代数上的行列式来描述。这种关系首先是在真正的监管者身上观察到的。后者有$p$ -adic类似物，然后定义了$p$ -adic熵和$p$ -adic行列式，以便在真实情况下保持类似的关系。我们描述了这$p$ -进理论在第二部分的文件。除了3.1节中的一些结果外，本说明几乎完全是对已知结果的综述。然而，该理论的不同方面以前没有一起讨论过。一路上，我们指出了几个开放的问题和进一步研究的可能方向。
英文摘要：
In this note we describe instances where values of the $K$-theoretical regulator map evaluated on topological cycles equal entropies of topological actions by a group $Γ$. These entropies can also be described by determinants on the von Neumann algebra of $Γ$. The relations were first observed for real regulators. The latter have $p$-adic analogues and both $p$-adic entropy and $p$-adic determinants were then defined so that similar relations hold as in the real case. We describe this $p$-adic theory in the second part of the paper. This note is almost entirely a survey of known results with the exception of some results in section 3.1. However the different aspects of the theory have not been discussed together before. Along the way we point out several open questions and possible directions for further research.
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