On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach

Katsuya Eda; Umed H. Karimov; Dušan Repovš

doi:10.1007/s00009-011-0165-1

On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach

Katsuya Eda, Umed H. Karimov, Dušan Repovš^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π₁(X, x) is trivial if and only if π₂(AC(X, x)) is trivial. As a corollary, AC(S¹, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

Original language	English
Pages (from-to)	519-528
Number of pages	10
Journal	Mediterranean Journal of Mathematics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s00009-011-0165-1
Publication status	Published - 2013 Feb

Keywords

Alternating cone
asphericity
cell-like space
Noncontractible compactum
Peano continuum
Snake cone
Topologist sine curve
trivial shape
weak homotopy equivalence

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00009-011-0165-1

Cite this

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title = "On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach",

abstract = "We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.",

keywords = "Alternating cone, asphericity, cell-like space, Noncontractible compactum, Peano continuum, Snake cone, Topologist sine curve, trivial shape, weak homotopy equivalence",

author = "Katsuya Eda and Karimov, {Umed H.} and Du{\v s}an Repov{\v s}",

year = "2013",

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doi = "10.1007/s00009-011-0165-1",

language = "English",

volume = "10",

pages = "519--528",

journal = "Mediterranean Journal of Mathematics",

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TY - JOUR

T1 - On 2-dimensional Nonaspherical Cell-like Peano Continua

T2 - A Simplified Approach

AU - Eda, Katsuya

AU - Karimov, Umed H.

AU - Repovš, Dušan

PY - 2013/2

Y1 - 2013/2

N2 - We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

AB - We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

KW - Alternating cone

KW - asphericity

KW - cell-like space

KW - Noncontractible compactum

KW - Peano continuum

KW - Snake cone

KW - Topologist sine curve

KW - trivial shape

KW - weak homotopy equivalence

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VL - 10

SP - 519

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 1

ER -

On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach

Abstract

Keywords

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