Honam Mathematical Journal (호남수학학술지)

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SOME MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS

  • Im, Young-Ho (Department of Mathematics, Pusan National University)
  • Received : 2007.05.12
  • Accepted : 2007.08.03
  • Published : 2007.09.25
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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 some algebraic conditions and X(N) $\neq$ 0 is a codimension-(2t + 2) PL fibrator.

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References

  1. D. S. Coram and P. F. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977) 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) 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, Hyperhopfian groups and approximate fibrations, Compositio Math. 86 (1993) 159-176
  5. R. J. Daverman, Manifolds that induce approximate fibrations in the PL category, Topology Appl. 66 (1995) 267-297 https://doi.org/10.1016/0166-8641(95)00051-H
  6. R. J. Daverman, Real projective spaces are nonfibrarors, Topology Appl. 94 (1999) 61-66. https://doi.org/10.1016/S0166-8641(98)00025-X
  7. R. J. Daverman, Y. H. Im and Y. Kim, Connected sums of 4-manifolds as $codimension-{\kappa}$ fibrators, J. London Math. Soc. (2) 68 (2003) 206-222 https://doi.org/10.1112/S0024610703004332
  8. Y.H. Im and Y. Kim, Hopfian and strongly hopfian manifolds, Fund. Math. 159 (1999) 127-134
  9. Y.H. Im and Y. Kim, Partially aspherical manifolds with nonzero Euler characteristic as PL fibrators, J. Korean Math. Soc. 43 (2006) 99-109 https://doi.org/10.4134/JKMS.2006.43.1.099
  10. 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
  11. Y. Kim, Connected sums of manifolds which induce approximate fibrations, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1497-1506. https://doi.org/10.1090/S0002-9939-00-05385-5
  12. J. Milnor, Infinite cyclic coverings, in Conference on the topology of manifolds (J. G. Hocking, ed.), Prindle Weber & Schmidt, Inc., Boston, 1968,115-133
  13. S. Rosset, A vanishing theorem for Euler characteristics, Math. Z. 185 (1984) 211-215 https://doi.org/10.1007/BF01181691
  14. E. H. Spanier, Algebraic Topology, McGraw-Hill Book Co., New York, 1966