On the Singular Homology of One Class of Simply-connected Cell-like Spaces

Katsuya Eda; Umed H. Karimov; Dušan Repovš

doi:10.1007/s00009-010-0079-3

On the Singular Homology of One Class of Simply-connected Cell-like Spaces

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

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(-,-) defined on the category of all spaces with base points and continuous mappings. For the circle S¹, the space SC(S¹, *) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces SC(Z, *) for any path-connected compact spaces Z.

Original language	English
Pages (from-to)	153-160
Number of pages	8
Journal	Mediterranean Journal of Mathematics
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s00009-010-0079-3
Publication status	Published - 2011 Jun

Keywords

asphericity
cell-likeness
continuum
free σ-product of groups
semi-local strong contractibility
simple connectivity
Snake space
Topologist sine curve
van Kampen theorem

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00009-010-0079-3

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title = "On the Singular Homology of One Class of Simply-connected Cell-like Spaces",

abstract = "In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(-,-) defined on the category of all spaces with base points and continuous mappings. For the circle S1, the space SC(S1, *) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces SC(Z, *) for any path-connected compact spaces Z.",

keywords = "asphericity, cell-likeness, continuum, free σ-product of groups, semi-local strong contractibility, simple connectivity, Snake space, Topologist sine curve, van Kampen theorem",

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

year = "2011",

month = jun,

doi = "10.1007/s00009-010-0079-3",

language = "English",

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AU - Eda, Katsuya

AU - Karimov, Umed H.

AU - Repovš, Dušan

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N2 - In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(-,-) defined on the category of all spaces with base points and continuous mappings. For the circle S1, the space SC(S1, *) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces SC(Z, *) for any path-connected compact spaces Z.

AB - In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(-,-) defined on the category of all spaces with base points and continuous mappings. For the circle S1, the space SC(S1, *) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces SC(Z, *) for any path-connected compact spaces Z.

KW - asphericity

KW - cell-likeness

KW - continuum

KW - free σ-product of groups

KW - semi-local strong contractibility

KW - simple connectivity

KW - Snake space

KW - Topologist sine curve

KW - van Kampen theorem

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 2

ER -

On the Singular Homology of One Class of Simply-connected Cell-like Spaces

Abstract

Keywords

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