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Any 3-manifold 1-dominates at most finitely many 3-manifolds of $S^3$-geometry

Authors: Claude Hayat-Legrand, Shicheng Wang and Heiner Zieschang
Journal: Proc. Amer. Math. Soc. 130 (2002), 3117-3123
MSC (2000): Primary 55M25, 54C05, 57M05
Published electronically: March 14, 2002
MathSciNet review: 1908938
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Abstract: Any 3-manifold 1-dominates at most finitely many 3-manifolds supporting $S^3$ geometry.

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

  • 1. Boileau M. and Wang S.C. Nonzero degree maps and surface bundles over $S^1$, J. Diff. Geom. 43 (1996), 789-908. MR 98g:57023
  • 2. Browder, W.: Surgery on simply-connected manifolds. Berlin-Heidelberg-New York: Springer 1972. MR 50:11272
  • 3. Kirby, R.: Problems in low-dimensional topology. Geometric topology, Edited by H. Kazez, AMS/IP Vol. 2., International Press, 1997. MR 98f:57001
  • 4. Hayat-Legrand, C.; Wang, S.C. and Zieschang, H.: Degree one maps onto Lens Spaces. Pacific J. Math. 176, 19-32 (1996) MR 98b:57030
  • 5. Munkres, J., Elements of Algebraic Topology. Addison-Wesley Publish Company 1984. MR 85m:55001
  • 6. Neumann, W.D. and Raymond, F., Seifert manifolds, plumbing, $\mu$-invariant and orientation reversing maps, Lect. Note in Math. 664, 162-195, Springer, 1978. MR 80e:57008
  • 7. Reid, A. and Wang, S.C., Non-Haken 3-manifolds is not larger with respect to mappings of nonzero degree, Comm. Analy. Geom. Vol. 7, No. 1, 105-132 (1999). MR 2000c:57042
  • 8. Rong, Y. Degree one maps between geometric $3$-manifolds. Trans. Amer. Math Soc, 322 411-436 (1992). MR 92j:57007
  • 9. Rong, Y. Maps between Seifert fibered spaces of infinite $\pi_1$. Pacific J. Math. 160, 143-154 (1993). MR 94e:55026
  • 10. Rong, Y. Degree one maps of Seifert manifolds and a note on Seifert volume, Topology and its Application. Vol. 64 No. 2 191-200 (1995). MR 96c:57034
  • 11. Scott, G.P., The geometries of $3$-manifolds. Bull. London Math. Soc. 15, 401-487 (1983).
  • 12. Seifert, H. and Threlfall, W., A text book of topology (English transl.) Academic Press 1980. MR 82b:55001
  • 13. Soma, T., Nonzero degree maps to hyperbolic 3-manifolds, J. Diff. Geom. 49 (1998), 517-546. MR 2000b:57034
  • 14. Soma, T., Sequences of degree-one maps between geometric 3-manifolds, Math. Annalen. 316, (2000) 733-742. MR 2001b:57039
  • 15. Spanier, E., Algebraic Topology. McGraw-Hill Book Comp., New York, N.Y. 1966. MR 35:1007
  • 16. Wang, S.C. and Zhou, Q., Any $3$-manifold $1$-dominates only finitely Seifert manifolds with infinite $\pi_1$. Math. Annalen, in press.

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Additional Information

Claude Hayat-Legrand
Affiliation: Department of Mathematics, University of Sabatier, Toulouse 31062, France

Shicheng Wang
Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China

Heiner Zieschang
Affiliation: Department of Mathematics, Ruhr University, Bochum 44780, Germany

Keywords: 3-manifold, degree one map
Received by editor(s): November 17, 2000
Received by editor(s) in revised form: May 23, 2001
Published electronically: March 14, 2002
Additional Notes: The second author was partially supported by MSTC and Outstanding Youth Fellowships of NSFC
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society

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