Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Crystallisations of $ 2$-fold branched coverings of $ S\sp{3}$

Author: Massimo Ferri
Journal: Proc. Amer. Math. Soc. 73 (1979), 271-276
MSC: Primary 57Q15; Secondary 57M12, 57M15, 57N10
MathSciNet review: 516477
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] J. S. Birman, Braids, links and mapping class groups, Ann. of Math. Studies, no. 82, Princeton Univ. Press, Princeton, N.J., 1975. MR 0375281 (51:11477)
  • [BH] J. S. Birman and H. M. Hilden, Heegaard splittings of branched coverings of $ {S^3}$, Trans. Amer. Math. Soc. 213 (1975), 315-352. MR 0380765 (52:1662)
  • [F] M. Ferri, Una rappresentazione delle n-varieta' topologiche triangolabili mediante grafi $ (n + 1)$-colorati, Boll. Un. Mat. Ital. 13 (1976), 250-260. MR 0428336 (55:1361)
  • [FG$ _{1}$] M. Ferri and C. Gagliardi, Alcune proprieta' caratteristiche delle triangolazioni contratte, Atti Sem. Mat. Fis. Univ. Modena 24 (1976), 195-220. MR 0436157 (55:9107)
  • [FG$ _{2}$] -, A graph-theoretical representation of closed PL manifolds, Proc. of the Second Conference on Geometric Topology (Univ. of Sussex, Brighton, 1977) (to appear).
  • [HW] P. J. Hilton and S. Wylie, An introduction to algebraic topology-Homology theory, Cambridge Univ. Press, London, 1960. MR 0115161 (22:5963)
  • [G] C. Gagliardi, How to deduce the fundamental group of a closed n-manifold from a contracted triangulation (to appear). MR 586313 (81m:57014)
  • [P$ _{1}$] M. Pezzana, Sulla struttura lopologica delle varieta' compatte, Atti Sem. Mat. Fis. Univ. Modena 23 (1975), 269-277. MR 0402792 (53:6606)
  • [P$ _{2}$] -, Diagrammi di Heegaard e triangolazione contratta, Boll. Un. Mat. Ital. 12 (1975), 98-105. MR 0425969 (54:13918)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57Q15, 57M12, 57M15, 57N10

Retrieve articles in all journals with MSC: 57Q15, 57M12, 57M15, 57N10

Additional Information

Keywords: Branched covering spaces, Heegaard splittings, links, plats, bridge presentation, graph, contracted triangulations, crystallisations
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society