The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.
In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing (#m(S1 x S2),ω) to be a Heegaard diagram by crystallization theory.
@article{urn:eudml:doc:44516,
title = {Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {435-457},
zbl = {1067.57014},
mrnumber = {MR2083964},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44516}
}
Casali, Maria Rita. Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 435-457. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44516/