Dotted Links, Heegaard Diagrams, and Colored Graphs for PL 4-manifolds

Resumen

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×S2), !), and the algorithmicity of the whole process depends on the effective possibility of recognizing (#m(S1×S2), !) to be a Heegaard diagram by crystallization theory.