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.
Heegaard diagrams, graphs and 3-manifold spines / Bandieri, Paola; Cavicchioli, Alberto; Grasselli, Luigi. - In: RADOVI MATEMATICKI. - ISSN 0352-6100. - STAMPA. - 4:(1988), pp. 383-402.
Heegaard diagrams, graphs and 3-manifold spines
BANDIERI, Paola;CAVICCHIOLI, Alberto;GRASSELLI, Luigi
1988
Abstract
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.
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