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1999 | 159 | 2 | 127-134
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Hopfian and strongly hopfian manifolds

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Let p: M → B be a proper surjective map defined on an (n+2)-manifold such that each point-preimage is a copy of a hopfian n-manifold. Then we show that p is an approximate fibration over some dense open subset O of the mod 2 continuity set C' and C' ∖ O is locally finite. As an application, we show that a hopfian n-manifold N is a codimension-2 fibrator if χ(N) ≠ 0 or $H_1(N) ≅ ℤ_2$
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autor
  • Department of Mathematics, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996-1300, U.S.A., ykim@math.utk.edu
Bibliografia
  • [1] G. Baumslag and D. Solitar, Some two-generator and one relator non-hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199-201.
  • [2] N. Chinen, Manifolds with nonzero Euler characteristic and codimension-2 fibrators, Topology Appl. 86 (1998), 151-167.
  • [3] N. Chinen, Finite groups and approximate fibrations, ibid., to appear.
  • [4] D. S. Coram and P. F. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288.
  • [5] D. S. Coram and P. F. Duvall, Approximate fibrations and a movability condition for maps, Pacific J. Math. 72 (1977), 41-56.
  • [6] D. S. Coram and P. F. Duvall, Mappings from $S^3$ to $S^2$ whose point inverses have the shape of a circle, Gen. Topology Appl. 10 (1979), 239-246.
  • [7] R. J. Daverman, Submanifold decompositions that induce approximate fibrations, Topology Appl. 33 (1989), 173-184.
  • [8] R. J. Daverman, Hyperhopfian groups and approximate fibrations, Compositio Math. 86 (1993), 159-176.
  • [9] R. J. Daverman, Codimension-2 fibrators with finite fundamental groups, Proc. Amer. Math. Soc., to appear.
  • [10] R. J. Daverman, 3-manifolds with geometric structure and approximate fibrations, Indiana Univ. Math. J. 40 (1991), 1451-1469.
  • [11] J. C. Hausmann, Geometric Hopfian and non-Hopfian situations, in: Lecture Notes in Pure and Appl. Math. 105, Marcel Dekker, New York, 1987, 157-166.
  • [12] J. C. Hausmann, Fundamental group problems related to Poincaré duality, in: CMS Conf. Proc. 2, Amer. Math. Soc., Providence, R.I., 1982, 327-336.
  • [13] J. Hempel, 3-manifolds, Ann. of Math. Stud. 86, Princeton Univ. Press, Princeton, N.J., 1976.
  • [14] R. Hirshon, Some results on direct sum of hopfian groups, Ph.D. Dissertation, Adelphi Univ., 1967.
  • [15] Y. H. Im, Products of surfaces that induce approximate fibrations, Houston J. Math. 21 (1995), 339-348.
  • [16] Y. Kim, Strongly hopfian manifolds as codimension-2 fibrators, Topology Appl., to appear.
  • [17] Y. Kim, Manifolds with hyperhopfian fundamental group as codimension-2 fibrators, ibid., to appear.
  • [18] A. N. Parshin and I. R. Shafarevich, Algebra VII, Encyclopaedia Math. Sci. 58, Springer, 1993.
  • [19] J. Roitberg, Residually finite, hopfian and co-hopfian spaces, in: Contemp. Math. 37, Amer. Math. Soc., 1985, 131-144.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv159i2p127bwm
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