  We test the efficiency of applying Geometric Deep Learning to the problems in
low-dimensional topology in a certain simple setting. Specifically, we consider
the class of 3-manifolds described by plumbing graphs and use Graph Neural
Networks (GNN) for the problem of deciding whether a pair of graphs give
homeomorphic 3-manifolds. We use supervised learning to train a GNN that
provides the answer to such a question with high accuracy. Moreover, we
consider reinforcement learning by a GNN to find a sequence of Neumann moves
that relates the pair of graphs if the answer is positive. The setting can be
understood as a toy model of the problem of deciding whether a pair of Kirby
diagrams give diffeomorphic 3- or 4-manifolds.
