Crystallisations of 2-fold branched coverings of 𝑆³

Ferri, Massimo

doi:10.1090/S0002-9939-1979-0516477-6

Crystallisations of $2$-fold branched coverings of $S^{3}$
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by Massimo Ferri

Proc. Amer. Math. Soc. 73 (1979), 271-276

DOI: https://doi.org/10.1090/S0002-9939-1979-0516477-6

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Abstract:

We describe the construction of a crystallisation of a 2-fold cyclic covering space of ${S^3}$ branched over a link, from a bridge-presentation of the branch set.

References

Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
Joan S. Birman and Hugh M. Hilden, Heegaard splittings of branched coverings of $S^{3}$, Trans. Amer. Math. Soc. 213 (1975), 315–352. MR 380765, DOI 10.1090/S0002-9947-1975-0380765-8
Massimo Ferri, Una rappresentazione delle $n$-varietà topologiche triangolabili mediante grafi $(n+1)$-colorati, Boll. Un. Mat. Ital. B (5) 13 (1976), no. 1, 250–260. MR 0428336
Massimo Ferri and Carlo Gagliardi, Alcune proprietà caratteristiche delle triangolazioni contratte, Atti Sem. Mat. Fis. Univ. Modena 24 (1975), no. 2, 195–220 (1976). MR 0436157

A graph-theoretical representation of closed PL manifolds

P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161, DOI 10.1017/CBO9780511569289
Carlo Gagliardi, How to deduce the fundamental group of a closed $n$-manifold from a contracted triangulation, J. Combin. Inform. System Sci. 4 (1979), no. 3, 237–252 (English, with Italian summary). MR 586313
Mario Pezzana, Sulla struttura topologica delle varietà compatte, Atti Sem. Mat. Fis. Univ. Modena 23 (1974), no. 1, 269–277 (1975). MR 0402792
Mario Pezzana, Diagrammi di Heegaard e triangolazione contratta, Boll. Un. Mat. Ital. (4) 12 (1975), no. 3, suppl., 98–105 (Italian, with English summary). Collection in memory of Enrico Bompiani. MR 0425969