An equivalence criterion for 3-manifolds

Within geometric topology of 3-manifolds (with or withoutboundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called "dipole moves". Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting