Preprint\(PD_3\)groups and HNN extensionsJonathan A. HillmanAbstractWe show that if a \(PD_3\)group \(G\) splits as an HNN extension \(A*_C\varphi\) where \(C\) is a \(PD_2\)group then the Poincaré dual in \(H^1(G;\mathbb{Z})= \mathrm{Hom}(G,\mathbb{Z})\) 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. Keywords: fundamental class, HNN extension, \(PD_3\)group, surface group.AMS Subject Classification: Primary 57N13.
This paper is available as a pdf (292kB) file.
