论文标题
$ PD_3 $ - 组和HNN扩展
$PD_3$-groups and HNN Extensions
论文作者
论文摘要
我们表明，如果$ pd_3 $ -group $ g $ split作为hnn扩展$ a*_cφ$其中$ c $是$ pd_3 $ - group，则$ h^1（g; \ m m i \ mathbb {z}）中的poincarédual， $ f：g \ to \ mathbb {z} $带有内核的正常闭合$ a $。我们还对$ PD_3 $ -Groups进行了其他几种观察，这些观察结果分裂在$ PD_2 $ -Groups上。
We show that if a $PD_3$-group $G$ splits as an HNN extension $A*_Cφ$ where $C$ is a $PD_3$-group then the Poincaré dual in $H^1(G;\mathbb{Z})=Hom(G,\mathbb{Z})$ of the homology class $[C]$ is the epimorphism $f:G\to\mathbb{Z}$ with kernel the normal closure of $A$. We also make several other observations about $PD_3$-groups which split over $PD_2$-groups.
