Free \({\mathbb{Q}}/{\mathbb{Z}}\) actions (Q1095461)

The author studies in this interesting paper the free action of the group \({\mathbb{Q}}/{\mathbb{Z}}\) on simply connected manifolds. The paper contains several results on the free action of \({\mathbb{Q}}/{\mathbb{Z}}\) as a consequence of the free action of the cyclic group \({\mathbb{Z}}_ n\). There are also some results on the free action of the group \({\mathbb{Z}}[1/p]/{\mathbb{Z}}.\) There are applicatons to the properties of closed manifolds. Homotopy theory and obstructions of free \({\mathbb{Q}}/{\mathbb{Z}}\) action on certain manifolds are studied. There is a discussion of free actions of \({\mathbb{Z}}_ n\) (and as a consequence the free action of \({\mathbb{Q}}/{\mathbb{Z}}\)) on noncompact manifolds and a list of some open problems.