Isoperimetric inequalities for Poincar\'e duality groups

Dawid Kielak; Peter Kropholler

Isoperimetric inequalities for Poincar\'e duality groups

Group Theory 2021-03-18 v2 Geometric Topology

Authors: Dawid Kielak , Peter Kropholler

Abstract

We show that every oriented $n$ -dimensional Poincar\'e 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.

Keywords

mapping class groups lie groups algebraic varieties

Cite

@article{arxiv.2008.07812,
  title  = {Isoperimetric inequalities for Poincar\'e duality groups},
  author = {Dawid Kielak and Peter Kropholler},
  journal= {arXiv preprint arXiv:2008.07812},
  year   = {2021}
}

Comments

10 pages, 1 figure. v2: final part of the paper substantially expanded to accommodate referee's comments. To appear in Proc. Amer. Math. Soc

Isoperimetric inequalities for Poincar\'e duality groups

Abstract

Keywords

Cite

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