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arXiv · 2004.03803

$PD_3$-groups and HNN Extensions

Jonathan A. Hillman
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Abstract

We show that if a $PD_3$-group $G$ splits as an HNN extension $A*_C\varphi$ where $C$ is a $PD_3$-group then the Poincar\'e 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.

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Jonathan A. Hillman. 2020-04-08. $PD_3$-groups and HNN Extensions. https://arxiv.org/abs/2004.03803

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