# Hopfian and strongly hopfian manifolds

Fundamenta Mathematicae (1999)

- Volume: 159, Issue: 2, page 127-134
- ISSN: 0016-2736

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topIm, Young, and Kim, Yongkuk. "Hopfian and strongly hopfian manifolds." Fundamenta Mathematicae 159.2 (1999): 127-134. <http://eudml.org/doc/212324>.

@article{Im1999,

abstract = {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 $H_1(N) ≅ ℤ_2$},

author = {Im, Young, Kim, Yongkuk},

journal = {Fundamenta Mathematicae},

keywords = {strongly Hopfian manifold; approximate fibration; mod 2 continuity set; codimension-2 fibrator; Hopfian group; hyper-Hopfian group; residually finite group; proper map},

language = {eng},

number = {2},

pages = {127-134},

title = {Hopfian and strongly hopfian manifolds},

url = {http://eudml.org/doc/212324},

volume = {159},

year = {1999},

}

TY - JOUR

AU - Im, Young

AU - Kim, Yongkuk

TI - Hopfian and strongly hopfian manifolds

JO - Fundamenta Mathematicae

PY - 1999

VL - 159

IS - 2

SP - 127

EP - 134

AB - 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 $H_1(N) ≅ ℤ_2$

LA - eng

KW - strongly Hopfian manifold; approximate fibration; mod 2 continuity set; codimension-2 fibrator; Hopfian group; hyper-Hopfian group; residually finite group; proper map

UR - http://eudml.org/doc/212324

ER -

## References

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- [13] J. Hempel, 3-manifolds, Ann. of Math. Stud. 86, Princeton Univ. Press, Princeton, N.J., 1976.
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- [15] Y. H. Im, Products of surfaces that induce approximate fibrations, Houston J. Math. 21 (1995), 339-348. Zbl0841.57031
- [16] Y. Kim, Strongly hopfian manifolds as codimension-2 fibrators, Topology Appl., to appear. Zbl0930.57021
- [17] Y. Kim, Manifolds with hyperhopfian fundamental group as codimension-2 fibrators, ibid., to appear. Zbl0947.57025
- [18] A. N. Parshin and I. R. Shafarevich, Algebra VII, Encyclopaedia Math. Sci. 58, Springer, 1993.
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