Isoperimetric inequalities for Poincaré duality groups

Kielak, Dawid; Kropholler, Peter

doi:10.1090/proc/15596

Isoperimetric inequalities for Poincaré duality groups
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by Dawid Kielak and Peter Kropholler PDF

Proc. Amer. Math. Soc. 149 (2021), 4685-4698 Request permission

Abstract:

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.

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