论文标题
自由循环基团和二维右角Artin组的最小体积熵
Minimal volume entropy of free-by-cyclic groups and 2-dimensional right-angled Artin groups
论文作者
论文摘要
令$ g $为一个自由循环集团或二维右角Artin组。我们为每种非球体构成型的非球体简单复合物与$ g $具有最小的体积熵相当于0。在非呈现情况下，我们为这两种类别的最小值较小的小小的减小的小型熵提供了一个正面的下层。我们的结果依赖于二维统一指数生长的二维群体的最小体积熵的标准。通过分析纤维$π_1$生长崩溃和Babenko-Sabourau的非碰撞假设来显示此标准。
Let $G$ be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to $G$ has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criterion is shown by analyzing the fiber $π_1$-growth collapse and non-collapsing assumptions of Babenko-Sabourau.
