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Uncountably many quasi-isometry classes of groups of type FP
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 142, Number 6, December 2020
- pp. 1931-1944
- 10.1353/ajm.2020.0048
- Article
- Additional Information
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.