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.

中文翻译：

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无数 FP 类型群的准等距类

摘要：在较早的一篇论文中，其中一位作者为每个 $n\\geq 4$ 构建了不可数族的 $FP$ 类型群和 $n$ 维 Poincar\\'e 对偶群。我们表明这些组包括无数的准等距类。我们推断，对于每个 $n\\geq 4$，有无数的准等距类非循环 $n$-流形允许自由共紧适当不连续的离散群动作。