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.
An equivalence criterion for 3-manifolds / Casali, Maria Rita. - In: REVISTA MATEMÁTICA DE LA UNIVERSIDAD COMPLUTENSE DE MADRID. - ISSN 0214-3577. - STAMPA. - 10:(1997), pp. 129-147.