论文标题
实际上是RFRS映射Tori和连贯性
Virtually RFRS Mapping Tori and Coherence
论文作者
论文摘要
令$ g $为有限的组，可以写为扩展名\ [1 \ longrightArrow k \ longrightArrow g \ longrightArrow f_2 \ longrightArrow 1 \]，其中$ k $是有限生成的免费组$ f_n $，$ n> 2 $，或者是$ n> 2 $的基本组，或者是封闭式的基本组。 We prove that if the image of the monodromy map $ρ\colon F_2 \to \operatorname{Out(K)}$ contains an element $φ\in \operatorname{Out(K)}$ such that the mapping torus $K \rtimes_φ \Bbb{Z}$ is virtually residually finite rationally solvable (for instance whenever the mapping torus is双曲线），然后$ g $是不连贯的。特别是，当图像纯粹是映射类组的纯粹的Anosov免费亚组时，这尤其适用。
Let $G$ be a finitely presented group that can be written as an extension \[ 1 \longrightarrow K \longrightarrow G \longrightarrow F_2 \longrightarrow 1 \] where $K$ is either the finitely generated free group $F_n$, $n > 2$ or the fundamental group of a closed surface of genus $g > 1$. We prove that if the image of the monodromy map $ρ\colon F_2 \to \operatorname{Out(K)}$ contains an element $φ\in \operatorname{Out(K)}$ such that the mapping torus $K \rtimes_φ \Bbb{Z}$ is virtually residually finite rationally solvable (for instance whenever the mapping torus is hyperbolic), then $G$ is not coherent. This applies, in particular, when the image is a purely pseudo--Anosov free subgroups of the mapping class group.
