Ascending HNN-extensions and properly 3-realisable groups

Abstract

In this paper, we show that any ascending HNN-extension of a finitely presented group is properly 3-realisable. We recall that a finitely presented group G is said to be properly 3-realisable if there exists a compact 2-polyhedron K with π1(K) ≅ G and whose universal cover K̃ has the proper homotopy type of a (PL) 3-manifold (with boundary).