论文标题
Sur L'Entropie volumique des Groupes deprésentationfinie
Sur l'entropie volumique des groupes de présentation finie
论文作者
论文摘要
在文章\ cite {bm1.22}中，为每组有限的表现引入了最小体积熵，我们在那里研究了其一些一般属性。最近在\ cite {bc21}中定义了几何有限基的最小体积熵的另一个概念。在本文中，我们对这两个概念进行了比较分析，如果几何维度等于$ 1 $，它们是重合的；它们的尺寸非常接近$ 2 $，但在其他情况下它们的差异很大。最后，我们介绍了一类称为软组的组，为此我们计算\ cite {bm1.22}中定义的最小体积熵。该类包含几个已知的组，例如，广义的baumslag-solitare组以及$ sl（2，\ mathbb {z}）$。通常，在\ cite {bc21}中定义的体积熵不适用于软组。
In the article \cite{BM1.22}, the minimum volume entropy is introduced for each group of finite presentation and there we study some of its general properties. Another concept of minimum volume entropy for geometrically finite groups has recently been defined in \cite{BC21}. In this paper, we present a comparative analysis of these two notions which coincide if the geometric dimension is equal to $1$; they are quite close in dimension $2$ but they differ radically in the other cases. Finally, we introduce a class of groups called soft groups, for which we calculate the minimum volume entropy defined in \cite{BM1.22}. This class contains several known groups, for example, generalized Baumslag-Solitare groups as well $SL(2,\mathbb{Z})$. The volume entropy defined in \cite{BC21}, in general, does not apply to soft groups.
