Full paper in PDF:
$%M. R. Casali, An equivalence criterion for 3-manifolds, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 129–147.%$

Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-colored graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-colored 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 -dimensional setting.

1991 Mathematics Subject Classification: 57Q15, 57N10, 57M15, 05C10.