有限性质和相对双曲群

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-26 DOI:10.1112/blms.70039

Harsh Patil

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引用次数: 0

摘要

我们证明了F n$ F_n$和FP n$ FP_n$对一个相对双曲群成立当且仅当它们对所有外围子群成立。作为一个应用，我们证明了至少存在可数多个不同的拟等距类，它们是F n$ F_n$型，但不是F n + 1型$F_{n+1}$和类似的FP n$ FP_n$类型，而不是FP n+1$FP_{n+1}$适用于所有正整数n$ n$。

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Finiteness properties and relatively hyperbolic groups

We show that properties $F_{n}$ and $F P_{n}$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended non-amenable groups that are type $F_{n}$ but not $F_{n + 1}$ and similarly of type $F P_{n}$ and not $F P_{n + 1}$ for all positive integers $n$ .