Strongly hopfian manifolds as codimension-2 fibrators

Yongkuk Kim

doi:10.1016/s0166-8641(97)00251-4

Strongly hopfian manifolds as codimension-2 fibrators

Yongkuk Kim

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

11 Scopus citations

Abstract

If a closed n-manifold N has a 2-1 covering, we consider the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups H_i of index 2 in π₁ (N), i.e., H = ∩_iεI H_i with [π₁(N) : H_i] = 2 for i ε I. We will show that if π₁(N) is residually finite, X(N) ≠ 0, and Ñ is hopfian, then N is a codimension-2 fibrator. And then, we will also get several results about codimension-2 fibrators as its corollaries.

Original language	English
Pages (from-to)	237-245
Number of pages	9
Journal	Topology and its Applications
Volume	92
Issue number	3
DOIs	https://doi.org/10.1016/s0166-8641(97)00251-4
State	Published - 1999

Keywords

Approximate fibration
Codimension-2 fibrator
Continuity sets
Degree one mod 2 map
Hopfian manifold
Residually finite group

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10.1016/s0166-8641(97)00251-4

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title = "Strongly hopfian manifolds as codimension-2 fibrators",

abstract = "If a closed n-manifold N has a 2-1 covering, we consider the covering space {\~N} of N corresponding to H, where H is the intersection of all subgroups Hi of index 2 in π1 (N), i.e., H = ∩iεI Hi with [π1(N) : Hi] = 2 for i ε I. We will show that if π1(N) is residually finite, X(N) ≠ 0, and {\~N} is hopfian, then N is a codimension-2 fibrator. And then, we will also get several results about codimension-2 fibrators as its corollaries.",

keywords = "Approximate fibration, Codimension-2 fibrator, Continuity sets, Degree one mod 2 map, Hopfian manifold, Residually finite group",

author = "Yongkuk Kim",

year = "1999",

doi = "10.1016/s0166-8641(97)00251-4",

language = "English",

volume = "92",

pages = "237--245",

journal = "Topology and its Applications",

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TY - JOUR

T1 - Strongly hopfian manifolds as codimension-2 fibrators

AU - Kim, Yongkuk

PY - 1999

Y1 - 1999

N2 - If a closed n-manifold N has a 2-1 covering, we consider the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups Hi of index 2 in π1 (N), i.e., H = ∩iεI Hi with [π1(N) : Hi] = 2 for i ε I. We will show that if π1(N) is residually finite, X(N) ≠ 0, and Ñ is hopfian, then N is a codimension-2 fibrator. And then, we will also get several results about codimension-2 fibrators as its corollaries.

AB - If a closed n-manifold N has a 2-1 covering, we consider the covering space Ñ of N corresponding to H, where H is the intersection of all subgroups Hi of index 2 in π1 (N), i.e., H = ∩iεI Hi with [π1(N) : Hi] = 2 for i ε I. We will show that if π1(N) is residually finite, X(N) ≠ 0, and Ñ is hopfian, then N is a codimension-2 fibrator. And then, we will also get several results about codimension-2 fibrators as its corollaries.

KW - Approximate fibration

KW - Codimension-2 fibrator

KW - Continuity sets

KW - Degree one mod 2 map

KW - Hopfian manifold

KW - Residually finite group

UR - https://www.scopus.com/pages/publications/0012703238

U2 - 10.1016/s0166-8641(97)00251-4

DO - 10.1016/s0166-8641(97)00251-4

M3 - Article

AN - SCOPUS:0012703238

SN - 0016-660X

VL - 92

SP - 237

EP - 245

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

Strongly hopfian manifolds as codimension-2 fibrators

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Keywords

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