Undecidability of the freedom problem for 3-manifold groups

The m-freedom problem, m a positive integer, is said to be (algorithmically) decidable for a family of presentations of groups if there exists an algorithm that, for any given presentation from this family, tells us whether the corresponding group is free in m (free) generators or not. In the paper, it is proved that for any m greater than or equal to 13 the m-freedom problem is undecidable for the family of presentations of fundamental groups of all connected, compact, topological three-dimensional manifolds without boundary.