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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FP类型的组有无数类准等距类

摘要：

在较早的论文中，一位作者为每个$ n \ geq 4 $构造了不可数的类型为$ FP $的组和$ n $维的庞加莱对偶组。我们表明，这些组包含无数个准等距类。我们推论出，对于每个$ n \\ geq 4 $，有无数的准等距类的无环$ n $流形允许自由共紧凑地适当离散的离散组动作。