• Title, Summary, Keyword: approximate fibration

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APPROXIMATE FIBRATIONS AND NON-APPROXIMATE FIBRATIONS IN PL CATEGORY

  • Im, Young-Ho
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1077-1085
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    • 1996
  • This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

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PRODUCT SPACES THAT INDUCE APPROXIMATE FIBRATIONS

  • Im, Young-Ho;Kang, Mee-Kwang;Woo, Ki-Mun
    • Journal of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.145-154
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    • 1996
  • In the study of manifold decompositions, a central theme is to understand the source manifold taking advantage of the informations of a base space and a decomposition. The concepts of both Hurewicz fibrations and cell-like maps have played very important roles for investigating the mutual relations of three objects. But it is somewhat restrictive for a decomposition map to be cell-like because its inverse images must have trivial shapes.

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NECESSARY AND SUFFICIENT CONDITIONS FOR CODIMENSION-k MAPS TO BE APPROXIMATE FIBRATIONS

  • Im, Young-Ho
    • Communications of the Korean Mathematical Society
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    • v.18 no.2
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    • pp.367-374
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    • 2003
  • Let N be a Closed n-manifold with residually finite, torsion free $\pi$$_1$(N) and finite H$_1$,(N). Suppose that $\pi$$\_$k/(N)=0 for 1 < k < n-1. We show that N is a codimension-n PL fibrator if and only if N does not cover itself regularly and cyclically up to homotopy type, provided $\pi$$_1$(N) satisfies a certain condition.

MANIFOLDS WITH TRIVIAL HOMOLOGY GROUPS IN SOME RANGE AS CODIMENSION-K FIBRATORS

  • Im, Young-Ho
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.283-289
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    • 2010
  • Approximate fibrations provide a useful class of maps. Fibrators give instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that rational homology spheres with some additional conditions are codimension-k PL fibrators and PL manifolds with trivial homology groups in some range can be codimension-k (k > 2) PL fibrators.

SOME MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS

  • Im, Young-Ho
    • Honam Mathematical Journal
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    • v.29 no.3
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    • pp.327-339
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    • 2007
  • 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.

PRODUCTS OF MANIFOLDS AS CONDIMENSION k FINBRATORS

  • Im, Young-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.79-90
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    • 1999
  • In this paper, we show that any product of a closed orientable n-manifold $N_1$ with finite fundamental group and a closed orientable asgerical m-mainfold $N_2$ with hopfian fundamental group, where X($N_1$) and X($N_2$) are nonzero, is a condimension 2 fibrator. Moreover, if <$\pi_i(N_1)$=0 for 1$N_1\timesN_2$ is a codimension k PL fibrator.

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PRODUCT OF PL FIBRATORS AS CODIMENSION-k FIBRATORS

  • Im, Young-Ho;Kim, Yong-Kuk
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.289-295
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    • 2007
  • We describe some conditions under which the product of two groups with certain property is a group with the same property, and we describe some conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, we find some PL fibrators among the product of fibrators.