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Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.

Maria Rita Casali (2004)

Revista Matemática Complutense

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...

Embedded surfaces in the 3-torus

Allan L. Edmonds (2008)

Fundamenta Mathematicae

Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the more involved case when the surface is nonorientable.

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