论文标题
用于同源填充功能的粗嵌入定理
A coarse embedding theorem for homological filling functions
论文作者
论文摘要
我们在适当的有限条件下证明了粗嵌入的诱导同源性功能的不平等。主要结果的应用包括表征有限呈现的组可能会承认将其粗糙嵌入到一组几何尺寸$ 2 $中的双曲线群体中，具有有限呈现的二次dehn的有限呈现的子组的特征，具有几何尺寸$ 2 $，以及将Nilpotent组的nilpotent群体嵌入其他相同的成长组中，并将其分为相同的成长组。
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a coarse embedding into a hyperbolic group of geometric dimension $2$, characterizations of finitely presentable subgroups of groups with quadratic Dehn function with geometric dimension $2$, and to coarse embeddings of nilpotent groups into other nilpotent groups of the same growth and into hyperbolic groups.
