Products of hopfian manifolds and codimension-2 fibrators

Robert J. Daverman; Young Ho Im; Yongkuk Kim

doi:10.1016/s0166-8641(99)00008-5

Products of hopfian manifolds and codimension-2 fibrators

Robert J. Daverman
, Young Ho Im
, Yongkuk Kim

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

5 Scopus citations

Abstract

We describe several conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, the product F × A of a closed hopfian n-manifold F and a closed orientable aspherical m-manifold A is hopfian when either π₁(F) is solvable and χ(A) ≠ 0 or π₁(F) is finite. Also, the product of any rational homology n-sphere ∑ⁿ for which π₁ (∑ⁿ) is finite and a closed orientable n-manifold N with π_i(N) = 0 for 1 < i < n - 1 is hopfian. Using such facts we investigate conditions under which products of codimension-2 (orientable) fibrators are again codimension-2 (orientable) fibrators.

Original language	English
Pages (from-to)	323-338
Number of pages	16
Journal	Topology and its Applications
Volume	103
Issue number	3
DOIs	https://doi.org/10.1016/s0166-8641(99)00008-5
State	Published - 2000

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(99)00008-5

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title = "Products of hopfian manifolds and codimension-2 fibrators",

abstract = "We describe several conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, the product F × A of a closed hopfian n-manifold F and a closed orientable aspherical m-manifold A is hopfian when either π1(F) is solvable and χ(A) ≠ 0 or π1(F) is finite. Also, the product of any rational homology n-sphere ∑n for which π1 (∑n) is finite and a closed orientable n-manifold N with πi(N) = 0 for 1 < i < n - 1 is hopfian. Using such facts we investigate conditions under which products of codimension-2 (orientable) fibrators are again codimension-2 (orientable) fibrators.",

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

author = "Daverman, \{Robert J.\} and Im, \{Young Ho\} and Yongkuk Kim",

year = "2000",

doi = "10.1016/s0166-8641(99)00008-5",

language = "English",

volume = "103",

pages = "323--338",

journal = "Topology and its Applications",

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TY - JOUR

T1 - Products of hopfian manifolds and codimension-2 fibrators

AU - Daverman, Robert J.

AU - Im, Young Ho

AU - Kim, Yongkuk

PY - 2000

Y1 - 2000

N2 - We describe several conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, the product F × A of a closed hopfian n-manifold F and a closed orientable aspherical m-manifold A is hopfian when either π1(F) is solvable and χ(A) ≠ 0 or π1(F) is finite. Also, the product of any rational homology n-sphere ∑n for which π1 (∑n) is finite and a closed orientable n-manifold N with πi(N) = 0 for 1 < i < n - 1 is hopfian. Using such facts we investigate conditions under which products of codimension-2 (orientable) fibrators are again codimension-2 (orientable) fibrators.

AB - We describe several conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, the product F × A of a closed hopfian n-manifold F and a closed orientable aspherical m-manifold A is hopfian when either π1(F) is solvable and χ(A) ≠ 0 or π1(F) is finite. Also, the product of any rational homology n-sphere ∑n for which π1 (∑n) is finite and a closed orientable n-manifold N with πi(N) = 0 for 1 < i < n - 1 is hopfian. Using such facts we investigate conditions under which products of codimension-2 (orientable) fibrators are again codimension-2 (orientable) fibrators.

KW - Approximate fibration

KW - Codimension-2 fibrator

KW - Continuity set

KW - Degree one mod 2 map

KW - Hopfian manifold

KW - Hyperhopfian group

UR - https://www.scopus.com/pages/publications/0012745431

U2 - 10.1016/s0166-8641(99)00008-5

DO - 10.1016/s0166-8641(99)00008-5

M3 - Article

AN - SCOPUS:0012745431

SN - 0016-660X

VL - 103

SP - 323

EP - 338

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

Products of hopfian manifolds and codimension-2 fibrators

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Keywords

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