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 $S^3$.
1991
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
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/450769
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