One relator groups are semistable at infinity
Finitely generated 1-relator groups form an important class of groups of cohomological dimension 2. By an inductive argument with groups which either split as amalgamated free products or HNN-extensions the authors show that their 1-relator groups \(G\) are semistable at infinity. (This means that any two proper rays converging to the same end of some universal \(G\)-space are properly homotopic.) This result implies the important corollary that \(H^ 2(G,\mathbb{Z} G)\) is free abelian.
scientific article; zbMATH DE number 167785