It is well-known that every closed orientable 3-manifold $M^3$ is the 3-fold simple covering $M^3(K,\omega)$ of $S^3$ branched over a knot K: hence, $M^3$ may be visualized by the associated coloured knot $(K,\omega)$. On the other hand, PL-manifolds of arbitrary dimension may be represented by coloured graphs, via pseudosimplicial triangulations. The present paper produces an algorithm to construct a 4-coloured graph representing $M^3(K,\omega)$, directly 'drawn over' the coloured knot $(K,\omega)$.

Coloured knots and coloured graphs representing 3-fold simple coverings of S3 / Casali, Maria Rita. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 137(1995), pp. 87-98. [10.1016/0012-365X(93)E0145-T]

Coloured knots and coloured graphs representing 3-fold simple coverings of S3

CASALI, Maria Rita
1995

Abstract

It is well-known that every closed orientable 3-manifold $M^3$ is the 3-fold simple covering $M^3(K,\omega)$ of $S^3$ branched over a knot K: hence, $M^3$ may be visualized by the associated coloured knot $(K,\omega)$. On the other hand, PL-manifolds of arbitrary dimension may be represented by coloured graphs, via pseudosimplicial triangulations. The present paper produces an algorithm to construct a 4-coloured graph representing $M^3(K,\omega)$, directly 'drawn over' the coloured knot $(K,\omega)$.
137
87
98
Coloured knots and coloured graphs representing 3-fold simple coverings of S3 / Casali, Maria Rita. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 137(1995), pp. 87-98. [10.1016/0012-365X(93)E0145-T]
Casali, Maria Rita
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/450761
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact