Hopfian and strongly hopfian manifolds

Young Ho Im; Yongkuk Kim

doi:10.4064/fm-159-2-127-134

Hopfian and strongly hopfian manifolds

Young Ho Im, Yongkuk Kim

Pusan National University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 H₁(N) ≅ ℤ₂.

Original language	English
Pages (from-to)	127-134
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	159
Issue number	2
DOIs	https://doi.org/10.4064/fm-159-2-127-134
State	Published - 1999

Keywords

Approximate fibration
Codimension-2 fibrator
Continuity set
Degree one mod 2 map
Hopfian manifold
Hyperhopfian group
Strongly hopfian manifold

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10.4064/fm-159-2-127-134

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keywords = "Approximate fibration, Codimension-2 fibrator, Continuity set, Degree one mod 2 map, Hopfian manifold, Hyperhopfian group, Strongly hopfian manifold",

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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 H1(N) ≅ ℤ2.

KW - Approximate fibration

KW - Codimension-2 fibrator

KW - Continuity set

KW - Degree one mod 2 map

KW - Hopfian manifold

KW - Hyperhopfian group

KW - Strongly hopfian manifold

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JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

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ER -

Hopfian and strongly hopfian manifolds

Abstract

Keywords

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