The proper Lusternik–Schnirelmann category of semistable one-ended 3-manifolds

In this paper we give detecting elements for the proper Lusternik–Schnirelmann category of any missing boundary 3-manifold. As a consequence, we determine the proper LS category of all orientable one-ended semistable open 3-manifolds. These results extend those in Cárdenas et al. (2012) [10].