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PARTIALLY ASHPHERICAL MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS

  • Im, Young-Ho (Department of Mathematics Pusan National University) ;
  • Kim, Yong-Kuk (Department of Mathematics Kyungpook National University)
  • Published : 2006.01.01

Abstract

Approximate fibrations form a useful class of maps. By definition fibrators provide instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that every closed s-hopfian t-aspherical manifold N with sparsely Abelian, hopfian fundamental group and X(N) $\neq$ 0 is a codimension-(t + 1) PL fibrator.

References

  1. D. S. Coram and P. F. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), no. 2, 275-288 https://doi.org/10.1216/RMJ-1977-7-2-275
  2. R. J. Daverman, Submanifold decompositions that induce approximate fibrations, Topology Appl. 33 (1989), no. 2, 173-184 https://doi.org/10.1016/S0166-8641(89)80006-9
  3. R. J. Daverman, PL maps with manifold fibers, J. London Math. Soc. (2) 45 (1992), no. 1, 180-192 https://doi.org/10.1112/jlms/s2-45.1.180
  4. R. J. Daverman, Manifolds that induce approximate fibrations in the PL category, Topology Appl. 66 (1995), no. 3, 267-297 https://doi.org/10.1016/0166-8641(95)00051-H
  5. R. J. Daverman, Real projective spaces are nonfibrators, Special issue in memory of B. J. Ball. Topology Appl. 94 (1999), no. 1-3, 61-66 https://doi.org/10.1016/S0166-8641(98)00025-X
  6. R. J. Daverman, Y. H. Im, and Y. Kim, Connected sums of 4-manifolds as codimension-k fibrators, J. London Math. Soc. (2) 68 (2003), no. 1-2, 206-222 https://doi.org/10.1112/S0024610703004332
  7. Y. H. Im and Y. Kim, Hopfian and strongly hopfian manifolds, Fund. Math. 159 (1999), no. 2, 127-134
  8. Y. Kim, Strongly Hopfian manifolds as codimension-2 fibrators, Topology Appl. 92 (1999), no. 3, 237-245 https://doi.org/10.1016/S0166-8641(97)00251-4
  9. Y. Kim, Connected sums of manifolds which induce approximate fibrations, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1497-1506
  10. J. Milnor, Infinite cyclic coverings, 1968 Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) pp. 115-133 Prindle, Weber & Schmidt, Boston, Mass
  11. S. Rosset, A vanishing theorem for Euler characteristics, Math. Z. 185 (1984), no. 2, 211-215 https://doi.org/10.1007/BF01181691
  12. E. H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London 1966

Cited by

  1. SOME MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS vol.29, pp.3, 2007, https://doi.org/10.5831/HMJ.2007.29.3.327