同调填充函数的一个粗嵌入定理
A coarse embedding theorem for homological filling functions
摘要：
我们证明了在适当的有限性条件下，粗嵌入诱导同调Dehn函数的不等式。主要结果的应用包括刻画了哪些可表示群可以粗嵌入到几何维数为$2$的双曲群中，刻画了具有几何维数为$2$的二次Dehn函数的群的可表示子群，以及刻画了幂零群粗嵌入到具有相同增长的其他幂零群和双曲群中.
英文摘要：
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.
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