Complexes of non-positive curvature and automorphisms of the 4-punctured sphere
The author considers extensions of free groups \(F_3\) of rank three by \(\mathbb{Z}\) which can be realized as the fundamental group of the mapping torus of a 4-punctured sphere automorphism. There is a deformation retraction of the mapping torus to a 2-complex which carries a metric of non-positive curvature and the groups considered act cocompactly by isometries on the 2-complex thus giving a new proof of fact that these extension have automatic structures. A similar approach was used by the author to obtain such a result of \(\mathbb{Z}\)-extensions of rank two free groups.
scientific article; zbMATH DE number 938590