Questions on Attractors of 3-Manifolds

The attractor of a 3-manifold M3 is the set of all 3-gems which have a minimum number of vertices and induce M3. A gem (graph-encoded manifold) is a special edge graph which encodes a ball complex whose underlying space is a manifold. Every 3-manifold is induced by a 3-gem. In this article I briefly recall the definitions and terminology of 3-gems, state some of the properties of attractors and list a number basic open questions concerning them. The characteristic of this approach to 3-manifolds is the massive use of computers and so, most of the open questions here stated simply await proper implementation of algorithms to be answered.