论文标题
逐个自由和无曲的群体不连贯
Incoherence of free-by-free and surface-by-free groups
论文作者
论文摘要
令$ g $为半领产品$γ\ rtimes f_2 $，其中$γ$是免费组$ f_n $，$ n> 1 $，或者是基本组$ s_g $ s_g $ s $ g> 1 $。我们证明$ g $是不连贯的，解决了D. Wise提出的两个问题。这意味着对J. Hillman在表面上的地表束的基本组上的问题的肯定答案。尽管使用虚拟代数纤维显示了许多组是不一致的，但我们也表明，并非每个自由逐型组实际上都在代数纤维上。
Let $G$ be the semidirect product $Γ\rtimes F_2$ where $Γ$ is either the free group $F_n$, $n > 1$ or the fundamental group $S_g$ of a closed surface of genus $g > 1$. We prove that $G$ is incoherent, solving two problems posed by D. Wise. This implies an affirmative answer to a question of J. Hillman on the fundamental group of a surface bundle over a surface. Although many groups have been shown to be incoherent using virtual algebraic fibering, we also show that not every free-by-free group virtually algebraically fibers.
