Pacific Journal of Mathematics

Constructions of two-fold branched covering spaces.

José M. Montesinos and Wilbur Whitten

Article information

Source
Pacific J. Math., Volume 125, Number 2 (1986), 415-446.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102700086

Mathematical Reviews number (MathSciNet)
MR863536

Zentralblatt MATH identifier
0562.57004

Subjects
Primary: 57M12: Special coverings, e.g. branched
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Citation

Montesinos, José M.; Whitten, Wilbur. Constructions of two-fold branched covering spaces. Pacific J. Math. 125 (1986), no. 2, 415--446. https://projecteuclid.org/euclid.pjm/1102700086


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References

  • [BGM] J. Birman, F. Gonzalez-Acuna and J. M. Montesinos, Heegaard splittings of prime 3-manifolds are not unique, Michigan Math. J., 23 (1976), 97-103.
  • [Bl] Steven A. Bleiler, Knots prime on many strings, Trans. Amer. Math. Soc, (to appear).
  • [BoGM] M. Boileau, F. Gonzalez-Acuha and J. M. Montesinos, Surgery on double knots and symmetries, (to appear).
  • [BM] R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc, 155 (1971), 217-231.
  • [BuM] G. Burde and K. Murasugi, Links and Seifert fiber spaces, Duke Math. J., 37 (1970), 89-93.
  • [FS] S. Furusawa and M. Sakuma, Dehn surgery on symmetric knots, Math. Sem. Notes, 11 (1983), 179-198.
  • [G] F. Conzalez-Acuna, Ph.D. Thesis, Princeton University, 1969.
  • [GH] C. MeA. Gordon and Wolfgang Heil, Cyclic normal subgroups of fundamental groups of 3-manifolds,Topology,14 (1975), 305-309.
  • [GL] C. McA. Gordon and R. A. Litherland, Incompressible surfaces in branched coverings, Proceedings of the Symposium on the Smith Conjecture, Columbia University, (1978), 139-152.
  • [Ha] R. Hartley, Knots and involutions, Math. Zeit., 171 (1980),175-185.
  • [Ho] C. D. Hodgson, Involutions and isotopies of lens spaces, MS Thesis, University of Melbourne,1981.
  • [Ha] W. Jaco, Lectures on Three-Manifold Topology, Regional Conference Series43, Amer. Math. Soc,Providence, R. L,1980.
  • [JS] W. Jaco and P. Shalen, Seifert Fibered Spaces in 3-Manifolds, Memoirs of the Amer. Math. Soc,Vol. 21,No. 220,Amer. Math. Soc,Providence, R. I.,1979.
  • [Ki] P. K. Kim, Involutions on Klein spaces M(p, q), Trans. Amer. Math. Soc,268 (1981), 377-409.
  • [KTJP. K] Kim and J. L. Tollefson, PL involutions of fibered 3-manifolds, Trans. Amer. Math. Soc,232 (1977),221-237.
  • [KT2] Kim and J. L. Tollefson, Splitting the PL involutions of non-prime 3-manifolds, Michigan Math. J., 27 (1980),259-274.
  • [KwT] K. W. Kwun and J. L. Tollefson, Extending PL involutions of a compact manifold, Amer. J. Math., 99 (1977),995-1001.
  • [M] Jose M. Montesinos, Variedades de Seifert que son recubridores ciclicos rami- ficados de dos hojas, Bol. Soc.Math. Mexicana (2), 18 (1973), 1-32.
  • [Mo] Jose M. Montesinos, Sugery on links and double branched covers, Knots, Groups, and 3-Manifolds, Ann. of Math. Studies, 84, 227-259, Princeton University Press, Princeton, N.J.,1975.
  • [Mo2] Jose M. Montesinos, Sobre la representacion de variedades tridimensionales, unpublished preprint (1975).
  • [MS] W. H. Meeks and P. Scott, Finite group actions on 3-manifolds,preprint.
  • [MW] Jose M. Montesinos and W. Whitten, Constructions of two-fold branchedcover- ing spaces, Abstracts Amer. Math. Soc, 4 (Mar., 1983), Abstract 802-57-11, p. 178.
  • [Ru] J. H. Rubinstein, Representations of some 3-manifolds as 2-fold cyclicbranched covers ofS3, Notices Amer. Math. Soc,25 (1978), Abstract 78T-G7, A-18.
  • [Sa] M. Sakuma, Surface bundles over S1 which are 2-fold branched cyclic coverings ofS3, Math. Sem.notes, 9 (1981), 159-180.
  • [Sch] H. Schubert,Knotenund Vollringe, Acta Math., 90 (1953), 131-286.
  • [Ta] M. Takahashi, Two knots with the same two fold branched covering space, Yokohama Math. J., 25 (1977), 91-99.
  • [Tax] M. Takahashi, On homology spheres obtained by surgery on the figure-eight knot, Proc Sympos. Res. Inst. Math. Sci. Univ. Kyoto, 309 (1977) (in Japanese).
  • [Th] W. Thurston, The Geometry and Topology of 3-Manifolds, Lecture notes, Princeton University, 1978-1979.
  • [TolJJ.] Tollefson, involutions on S X S2 and other 3-manifolds, Trans. Amer. Math. Soc, 183 (1973), 139-152.
  • [Tol2] Tollefson, Involutions of Seifert fiber spaces, Pacific J. Math., 74 (1978), 519-529.
  • [Tol3] Tollefson, Involutions of sufficiently large 3-manifolds,Topoloy, 20 (1981), 323-352.
  • [Wa] F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I, II, Invent. Math., 3 (1967), 308-333; and Invent. Math., 4 (1967), 87-117.
  • [Wa2] F. Waldhausen, Uber Involutionen der 3-Sphre,Topology,8 (1969), 81-91.
  • [Wh] W. Whitten, Algebraic and geometric characterizationsof knots, Invent. Math., 26 (1974), 259-270.
  • [Wh2] W. Whitten, Inverting doubleknots, Pacific J. Math,97 (1981), 209-216.
  • [Zex] H. Zieschang, On extensions of fundamental groups of surfaces and related groups, Bull. Amer. Math. Soc,77 (1971), 1116-1119.
  • [Ze2] H. Zieschang, Addendum to: On extensions of fundamental groups of surfaces and related groups, Bull. Amer. Math. Soc,80 (1974), 366-367.