# Uncountably many quasi-isometry classes of groups of type FP

@article{Kropholler2020UncountablyMQ, title={Uncountably many quasi-isometry classes of groups of type FP}, author={Robert P. Kropholler and Ian J. Leary and Ignat Soroko}, journal={American Journal of Mathematics}, year={2020}, volume={142}, pages={1931 - 1944} }

Abstract:In an earlier paper, one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincar\\'e duality groups for each $n\\geq 4$. We show that those groups comprise uncountably many quasi-isometry classes. We deduce that for each $n\\geq 4$ there are uncountably many quasi-isometry classes of acyclic $n$-manifolds admitting free cocompact properly discontinuous discrete group actions.

## 7 Citations

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