For each integer g>1, a class $M_g$ of “2-symmetric” crystallizations, depending on a 2(g+1)-tuple of positive integers satisfying simple conditions is introduced; the “2-symmetry” implies that the represented closed, orientable 3-manifolds are 2-fold covering spaces of $S^3$ branched over a link. Since every closed, orientable 3-manifold M of Heegaard genus $g \le 2$ admits a crystallization belonging to $M_g$, we obtain an easy proof og the fact that M is a 2-fold covering spaces of $S^3$ branched over a link. Further, the class contains all Lins-Mandel crystallizations S(b,l,t,c), with l odd, which are thus proved to represent 2-fold branched coverings of $S^3$.

2-symmetric crystallizations and 2-fold branched coverings of S3 / Casali, Maria Rita; Grasselli, Luigi. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 87:(1991), pp. 9-22. [10.1016/0012-365X(91)90066-B]

2-symmetric crystallizations and 2-fold branched coverings of S3

CASALI, Maria Rita;GRASSELLI, Luigi
1991

Abstract

For each integer g>1, a class $M_g$ of “2-symmetric” crystallizations, depending on a 2(g+1)-tuple of positive integers satisfying simple conditions is introduced; the “2-symmetry” implies that the represented closed, orientable 3-manifolds are 2-fold covering spaces of $S^3$ branched over a link. Since every closed, orientable 3-manifold M of Heegaard genus $g \le 2$ admits a crystallization belonging to $M_g$, we obtain an easy proof og the fact that M is a 2-fold covering spaces of $S^3$ branched over a link. Further, the class contains all Lins-Mandel crystallizations S(b,l,t,c), with l odd, which are thus proved to represent 2-fold branched coverings of $S^3$.
87
9
22
2-symmetric crystallizations and 2-fold branched coverings of S3 / Casali, Maria Rita; Grasselli, Luigi. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 87:(1991), pp. 9-22. [10.1016/0012-365X(91)90066-B]
Casali, Maria Rita; Grasselli, Luigi
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: http://hdl.handle.net/11380/450769
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 14
social impact