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Virtually regular coverings

Authors: María Teresa Lozano and Carmen Safont
Journal: Proc. Amer. Math. Soc. 106 (1989), 207-214
MSC: Primary 57M12; Secondary 57M25
MathSciNet review: 937849
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Abstract: In this paper we introduce the concept of virtually regular covering, which include all regular branched coverings and also some irregular ones. We prove that, as in the case of regular coverings, some properties of the branching set reflect properties of the cover for virtually regular coverings of $ {S^3}$, generalizing results of Kim-Tollefson, Lozano and Plotnick. As a consequence, we obtain that every virtually regular cover of $ {S^3}$ branched along a fracturable prime and non split link is Haken.

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  • [1] C. McA. Gordon and R. A. Litherland, Incompressible surfaces in branched coverings, Symposium on the Smith Conjecture (Bass and Morgan, eds.) Academic Press, New York, 1984. MR 758466
  • [2] J. Hempel, $ 3$-manifolds, Ann. of Math. Stud., no. 86, Princeton Univ. Press, Princeton, N.J., 1976. MR 0415619 (54:3702)
  • [3] A. Hurwitz, Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891), 1-60. MR 1510692
  • [4] P. K. Kim and J. L. Tollefson, Spliting the PL involutions of nonprime $ 3$-manifolds, Michigan Math. J. 27 (1980), 259-274. MR 584691 (81m:57007)
  • [5] M. T. Lozano, Arcbodies, Math. Proc. Cambridge Philos. Soc. 94 (1983), 253-260. MR 715045 (85e:57004)
  • [6] M. T. Lozano and J. Przytycki, Incompressible surfaces in the exterior of a closed 3 braid. I, Math. Proc. Cambridge Philos. Soc. 98 (1985), 275-299. MR 795894 (87a:57013)
  • [7] M. T. Lozano and C. Safont, Sobre cubiertas localmente ciclicas, Contribuciones Matematicas. Estudios en honor del Profesor Botella. U. C. de Madrid (1986), 169-175. MR 873517 (88h:57012)
  • [8] W. H. Meeks III and S. T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. (2) 112 (1980), 441-484. MR 595203 (83d:53045)
  • [9] W. Meeks III, L. Simon and S. T. Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982), 621-659. MR 678484 (84f:53053)
  • [10] S. P. Plotnick, Finite group actions and nonseparating $ 2$-spheres, Proc. Amer. Math. Soc. 90 (1984), 430-432. MR 728363 (85f:57024)
  • [11] D. Rolfsen, Knots and links, Publish or Perish, Inc., 1976. MR 0515288 (58:24236)
  • [12] L. Villarreal, Recubridores localmente ciclicos, Tesis doctoral Univ. Complutense de Madrid (1984).
  • [13] -, Una variedad localmente ciclica que no es ciclica, Actas VII Congreso de Matemáticos de Expresión Latina, vol 1, 1986, pp. 525-528.
  • [14] -, Los recubridores localmente ciclicos no son universales (1985), preprint.

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Keywords: Branched coverings, incompressible surface, irreducible manifold, fracturable link
Article copyright: © Copyright 1989 American Mathematical Society

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