Within geometric topology of 3-manifolds (with or without boundary), 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.
@article{urn:eudml:doc:44240,
title = {An equivalence criterion for 3-manifolds.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {129-147},
zbl = {0878.57019},
mrnumber = {MR1452567},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44240}
}
Casali, M. R. An equivalence criterion for 3-manifolds.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 129-147. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44240/