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Degree one maps between hyperbolic small 3-manifolds


Authors: Michel Boileau and Shicheng Wang
Journal: Proc. Amer. Math. Soc. 135 (2007), 4023-4029
MSC (2000): Primary 57M50
DOI: https://doi.org/10.1090/S0002-9939-07-09265-9
Published electronically: September 5, 2007
MathSciNet review: 2341954
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct the first examples of degree one maps between non-homeomorphic closed hyperbolic small 3-manifolds.


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  • [BP] M. Boileau and J. Porti, Geometrization of 3-orbifolds of cyclic type, Astérisque Monograph, 272, 2001. MR 1844891 (2002f:57034)
  • [BW1] M. Boileau and S.C. Wang, Non-zero degree maps and surface bundles over $ S^1$, J. Diff. Geom. 43, 1996, 789-806. MR 1412685 (98g:57023)
  • [BW2] M. Boileau and S.C. Wang, Degree one maps between small 3-manifolds and Heegaard genus, Algebraic and Geometric Topology 5 (2005), no. 56, 1433-1450. MR 2171816 (2006f:57020)
  • [BoZ] M.Boileau and B. Zimmermann, Symmetries of nonelliptic Montesinos links, Math. Ann. 277, 1987, no. 3, 563-584. MR 891592 (88h:57004)
  • [BuZ] G. Burde and H. Zieschang, Knots, Walter de Gruyter Berlin, 1985 MR 808776 (87b:57004)
  • [CGLS] M. Culler, C. Gordon, J. Luecke, and P. Shalen, Dehn surgery on knots, Ann. of Math. 125, 1987, 237-300. MR 881270 (88a:57026)
  • [Dun1] N. Dunfield, A table of boundary slopes of Montesinos knots, Topology 40, 2001, 309-315. MR 1808223 (2001j:57008)
  • [Dun2] N. Dunfield, Cyclic surgery, degrees of maps of characters curves and volume rigidity for hyperbolic manifolds, Invent. Math. 136, 1999, 623-657. MR 1695208 (2000d:57022)
  • [Ga] D. Gabai, Detecting fibred links in $ S^3$, Comment. Math. Helv. 61, 1986, 519-555. MR 870705 (88c:57009)
  • [GL] C. Gordon and R. Litherland, Incompressible surfaces in branched coverings, in ``The Smith Conjecture'' (ed. by H. Bass, J.W. Morgan), Academic Press, 1984, pp. 139-152. MR 758466
  • [Hat] A. Hatcher, On the boundary curves of incompressible surfaces, Pac. J. Math. 99, 1982, 373-377. MR 658066 (83h:57016)
  • [HT] A. Hatcher and W. Thurston. Incompressible surfaces in 2-bridge knot complements, Invent. Math. 79, 1985, 225-246. MR 778125 (86g:57003)
  • [HWZ] C. Hayat-Legrand, S.C. Wang and H. Zieschang, Minimal Seifert manifolds, Math. Ann. 308, 673-700, 1997. MR 1464916 (98i:57029)
  • [Ka] A. Kawauchi, An imitation theory of manifolds, Osaka J. Math. 26, 1989, 447-464. MR 1021425 (90m:57026)
  • [Ja] W.H. Jaco Lectures on three-manifold topology, AMS, 1977. MR 0565450 (81k:57009)
  • [Mi] J. Milnor, The Schläfli differential equality, in Collected Papers, volume 1, Publish or Perish, 1994. MR 1277810 (95c:01043)
  • [Mo] J.M. Montesinos, Surgery on links and double branched covers of $ S^3$, in Knots, Groups and Manifolds, Ann. Math. Studies 84, 1975, 227-259. MR 0380802 (52:1699)
  • [O1] U. Oertel, Closed incompressible surfaces in complements of star links, Pac. J. Math. 111, 1984, 209-230. MR 732067 (85j:57008)
  • [O2] U. Oertel, Boundary slopes for Montesinos knots, Topology 28, 1989, 453-480. MR 1030987 (91e:57016)
  • [ORS] T. Ohtsuki, R. Riley and M Sakuma, Epimorphisms between 2-bridge link groups, Manuscript, June 2006.
  • [RW] R. Reid; S.C. Wang, Non-Haken $ 3$-manifolds are not large with respect to mappings of non-zero degree. Comm. Anal. Geom. 7 1999, no. 1, 105-132. MR 1674109 (2000c:57042)
  • [Ro] D. Rolfsen, Knots and Links, Publish or Perish, Berkeley, 1976. MR 0515288 (58:24236)
  • [Ru] D. Ruberman, Seifert surfaces of knots in $ S^4$, Pac. J. Math. 145, 1990, 97-116. MR 1066400 (91g:57024)
  • [Th] W. Thurston, Topology and Geometry of 3-manifolds, Princeton Lecture Notes, 1978.
  • [W] S.C. Wang, Non-zero degree one maps between 3-manifolds, Proceedings of ICM 2002, Vol. II (Beijing, 2002), 457-468, Higher Ed. Press, Beijing, 2002. MR 1957056 (2004a:57024)

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Additional Information

Michel Boileau
Affiliation: Laboratoire Émile Picard, CNRS UMR 5580, Université Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 4, France
Email: boileau@picard.ups-tlse.fr

Shicheng Wang
Affiliation: Department of Mathematics, LAMA, Peking University, Beijing 100871, People’s Republic of China
Email: wangsc@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-07-09265-9
Received by editor(s): March 16, 2006
Received by editor(s) in revised form: June 21, 2006
Published electronically: September 5, 2007
Additional Notes: The second author is partially supported by MSTC and NSFC
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2007 American Mathematical Society

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