DOI QR코드

DOI QR Code

THE PL FIBRATORS AMONG GEOMETRIC 4-MANIFOLDS

  • Kim, Yong-Kuk (Department of Mathematics Kyungpook National University)
  • Published : 2004.04.01

Abstract

Fibrators are closed manifolds which afford instant recognition of approximate fibrations. In this note we determine which 4-manifolds with geometric structure are fibrators.

Keywords

approximate fibration;codimension-k fibrator;geometric 4-manifold.

References

  1. J. London Math. Soc.(2) v.45 no.1 PL maps with manifold fibers https://doi.org/10.1112/jlms/s2-45.1.180
  2. Topology Appl. v.66 Complex projective spaces as PL fibrators https://doi.org/10.1016/0166-8641(95)00010-E
  3. Topology Appl. v.94 Real projective spaces are nonfibrators.Special issue in memory of B.J.Ball https://doi.org/10.1016/S0166-8641(98)00025-X
  4. J. London Math. Soc.(2) v.68 Connected sums of 4-manifolds as codimension-k fibrators R.J.Daverman;Y.H.Im;Y.Kim https://doi.org/10.1112/S0024610703004332
  5. Topology Appl. v.100 Complex surfaces which are fibre bundles https://doi.org/10.1016/S0166-8641(98)00085-6
  6. Topology v.31 Remarks on geometric structures on compact complex surfaces D.Kotschick https://doi.org/10.1016/0040-9383(92)90024-C
  7. Lecture Notes in Pure Appl. Math. Geometric hopfian and non-hopfian situations J.C.Hausmann
  8. Topology Appl. v.33 Submanifold decompositions that induce opproximate fibrations R.J.Daverman https://doi.org/10.1016/S0166-8641(89)80006-9
  9. Proc. Amer. Math. Soc. v.127 Codimension-2-fibrators with finite fundamental groups https://doi.org/10.1090/S0002-9939-99-05192-8
  10. Ann. of Math. Stud. v.111 Residual finiteness for 3-manifolds,Combinatorial group theory and topology(Alta,Utah,1984) J.Hampel;S.M.Gersten9ed.);J.R.Stallings(ed.)
  11. Fund. Math. v.159 Hopfian and strongly hopfian manifolds Y.H.Im;Y.Kim
  12. Bull. London Math. Soc, v.28 Nontorus knot groups are hyper-Hopfian D.S.Silver https://doi.org/10.1112/blms/28.1.4
  13. Topology Appl. v.52 On 4-manifolds with universal covering space S² ×R² or S³×R J.A.Hillman https://doi.org/10.1016/0166-8641(93)90088-U
  14. Topology Appl. v.96 Manifolds with hyperhopfian fundamental group as condimension-2 fibrators https://doi.org/10.1016/S0166-8641(98)00057-1
  15. The algebraic characterization of geometric 4-manifolds
  16. Topology v.25 Geometric structures on compact complex analytic surfaces C.T.C.Wall https://doi.org/10.1016/0040-9383(86)90035-2
  17. Topology Appl. v.102 3-manifolds fibering over the Klein bottle and codimension 2 orientable fibrators N.Chinen https://doi.org/10.1016/S0166-8641(98)00154-0
  18. Geometry & Topology Monographs v.5 Four-manifolds,geometries and knots
  19. Michigan Math. J. v.41 The PL fibrators among aspherical geometric 3-manifolds https://doi.org/10.1307/mmj/1029005081
  20. Topology Appl. v.56 Co-Hopficity of 3-manifold groups F.Gonzalez Acuna;W.Whitten https://doi.org/10.1016/0166-8641(94)90111-2
  21. Topology Appl. v.92 Strongly Hopfian manifolds as codimension-2 fibrators Y.Kim https://doi.org/10.1016/S0166-8641(97)00251-4
  22. J. Austral. Math. Soc. Ser. A v.68 Hyperbolic groups are hyperhopfian https://doi.org/10.1017/S1446788700001610
  23. Math. Z. v.117 The Hopf property of free products I.M.S.Dey;H.Neumann https://doi.org/10.1007/BF01109851
  24. Compositio Math. v.86 Hyperhopfian groups and approximate fibrations
  25. Proc. Amer. Math. Soc, v.129 Necessary and sufficient conditions for s-Hopfian manifolds to be condimension-2 fibrators https://doi.org/10.1090/S0002-9939-00-05998-0
  26. Four-dimensional geometries,Ph.D.Thesis,University of Warwick R.Filipkiewicz
  27. Topology Appl. v.75 On the homotopy types of closed 4-manifolds covered by S² ×R² https://doi.org/10.1016/S0166-8641(96)00099-5
  28. Topology Appl. To appear PL fibrator properties of partially aspherical manifolds
  29. Fibrator Properties of Manifolds Determined by their Fundamental Groups,Preprint R.J.Daverman;Y.Kim
  30. Topology Appl. v.66 Manifolds that induce approximate fibrations in the PL category https://doi.org/10.1016/0166-8641(95)00051-H
  31. Indiana Univ. Math. J. v.40 3-manifolds with geometric structure and approximate fibrations https://doi.org/10.1512/iumj.1991.40.40065
  32. J. London Math. Soc.(2) v.58 On 4-dimensional mapping tori and product geometries https://doi.org/10.1112/S0024610798006231