论文标题
庞加莱二元组的等量性不平等
Isoperimetric inequalities for Poincaré duality groups
论文作者
论文摘要
我们表明，每个面向$ n $二维的Poincaré二元组都超过了$*$ - ring $ r $，或者满足dimension $ n-1 $中的线性同级等级不平等。作为应用程序，我们证明当$ n = 2 $时，我们证明了此类组的山雀替代方案。然后，我们推断出一个新的证明，即当$ n = 2 $和$ r = \ mathbb z $时，所讨论的组是一个表面组。
We show that every oriented $n$-dimensional Poincaré duality group over a $*$-ring $R$ is amenable or satisfies a linear homological isoperimetric inequality in dimension $n-1$. As an application, we prove the Tits alternative for such groups when $n=2$. We then deduce a new proof of the fact that when $n=2$ and $R = \mathbb Z$ then the group in question is a surface group.
