Heegaard diagrams, graphs and 3-manifold spines. (English) Zbl 0709.57008
Summary: We study the relations between some well-known graph-theoretical representations of closed 3-manifolds as P-graphs, RR-systems, Heegaard diagrams and crystallizations. As a consequence of the interplay between the theories, we prove some theorems which improve the geometric knowledge of the named representations. Finally we show the strict connection of the results with the theory of 3-manifold spines.
MSC:
57N10 | Topology of general \(3\)-manifolds (MSC2010) |
57Q15 | Triangulating manifolds |
57M20 | Two-dimensional complexes (manifolds) (MSC2010) |
57Q40 | Regular neighborhoods in PL-topology |