Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

Yongkuk Kim

doi:10.1016/s0166-8641(98)00057-1

Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

Yongkuk Kim

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

8 Scopus citations

Abstract

Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups Hi,- of index 2 in π₁](N). First, we will show that if π₁(N) is hyperhopfian and Ñ is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.

Original language	English
Pages (from-to)	241-248
Number of pages	8
Journal	Topology and its Applications
Volume	96
Issue number	3
DOIs	https://doi.org/10.1016/s0166-8641(98)00057-1
State	Published - 1999

Keywords

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

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10.1016/s0166-8641(98)00057-1

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title = "Manifolds with hyperhopfian fundamental group as codimension-2 fibrators",

abstract = "Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space {\~N} of N corresponding to H, where H is the intersection of all subgroups Hi,- of index 2 in π1](N). First, we will show that if π1(N) is hyperhopfian and {\~N} is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.",

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

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T1 - Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

AU - Kim, Yongkuk

PY - 1999

Y1 - 1999

N2 - Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups Hi,- of index 2 in π1](N). First, we will show that if π1(N) is hyperhopfian and Ñ is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.

AB - Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups Hi,- of index 2 in π1](N). First, we will show that if π1(N) is hyperhopfian and Ñ is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.

KW - Approximate fibration

KW - Codimension-2 fibrator

KW - Continuity set

KW - Degree one mod 2 map

KW - Hopfian manifold

KW - Hyperhopfian group

UR - http://www.scopus.com/inward/record.url?scp=0012742616&partnerID=8YFLogxK

U2 - 10.1016/s0166-8641(98)00057-1

DO - 10.1016/s0166-8641(98)00057-1

M3 - Article

AN - SCOPUS:0012742616

SN - 0016-660X

VL - 96

SP - 241

EP - 248

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

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Keywords

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