Journal of Differential Geometry

Non-zero degree maps and surface bundles over $S\sp 1$

Michel Boileau and Shicheng Wang

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 43, Number 4 (1996), 789-806.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214458532

Digital Object Identifier
doi:10.4310/jdg/1214458532

Mathematical Reviews number (MathSciNet)
MR1412685

Zentralblatt MATH identifier
0868.57029

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Citation

Boileau, Michel; Wang, Shicheng. Non-zero degree maps and surface bundles over $S\sp 1$. J. Differential Geom. 43 (1996), no. 4, 789--806. doi:10.4310/jdg/1214458532. https://projecteuclid.org/euclid.jdg/1214458532


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References

  • [1] M.Boileau, M.Domergue and Y.Mathieu, Sur le complement d'un noeud homotope a zero, Preprint, 1995.
  • [2] W.Browder, Surgery on simple-connected manifolds, Springer, Berlin, 1972.
  • [3] R.Cowsik and G.Swarup, A remark on infinite cyclic covers, J. Pure Appl. Algebra 11 (1977) 131-138.
  • [4] A. Edmonds, Deformation of maps to branched coverings in dimension two, Ann. of Math. 110 (1979) 113-124.
  • [5] A. Edmonds and C. Livingston, Group actions on fibered three-manifolds, Comment. Math. Helv. 58 (1983) 529-542.
  • [6] D.Gabai, Detecting fibered link in S3, Comment. Math. Helv. 58 (1986) 519-554.
  • [7] D.Gabai, Detecting fibered link in S3, On 3-manifolds finitely covered bysurface bundle, London Math. Soc. Lecture Note Ser. 112 (1988) 145-154.
  • [8] D.Gabai, Detecting fibered link in S3, Foliations and the Topology of 3-manifolds. II, J. Differential Geom. 26 (1987) 461-478.
  • [9] J. Hempel, 3-manifolds, Ann. of Math. Stud., No.86Princeton University Press, 1976.
  • [10] C.Hayat-Legrand, S.Wang and H.Zieschang, Degree one map onto lens spaces, To appear in Pacific J. Math.
  • [11] E.Luft and Sjerve, Regular covering of homology 3-spheres by homology 3- spheres, Trans. Amer. Math. Soc. 311 (1987) 467-481.
  • [12] R. Myers, Simple knots in compact orientable 3-mamifolds, Trans. Amer. Math. Soc. 273 (1982) 75-92, 278 (1983) 271-288.
  • [13] R. Myers, Excellent 1-manifolds in compact 3-manifolds, Topology Appl. 49 (1993) 115-127.
  • [14] A. Reid, A non-Haken hyperbolic 3-manifold covered by a surface bundle, To appear in Pacific J. Math.
  • [15] T. Soma, Hyperbolic fibered links and fibre concordance, Math. Proc. Cambridge Philos. Soc. 96 (1984) 283-294.
  • [16] T. Soma, Virtual fiber groups in 3-manifold groups, J. London Math. Soc. (2) 43 (1991) 337-354.
  • [17] J. Stallings, On fibering certain 3-manifolds, Topology of 3-manifolds and related topics, Prentice-Hall, Englewood Cliffs, NJ, 1962.
  • [18] W. Thurston, Geometry and topology on 3-manifolds, Princeton note, 1979.
  • [19] W. Thurston, A norm for the homology of 3-manifolds, Memoirs of Amer. Math. Soc. 59 (1986) 100-130.
  • [20] W. Thurston, Hyperbolic structures on 3-manifolds. I: Deformation of acylindral manifolds, Ann. of Math. 124 (1986) 203-246.
  • [21] W. Thurston, Hyperbolic structures on 3-manifolds II : Surface groupes and 3-manifolds which fiber over the circle, Preprint, 1980.
  • [22] S. Wang, The existence of maps of non-zero degree between aspherical 3-manifolds, Math. Z. 208 (1991) 147-160.
  • [23] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56-88.