On snake cones, alternating cones and related constructions

Katsuya Eda; Umed H. Karimov; Dušan Repovš; Andreas Zastrow

doi:10.3336/gm.48.1.11

On snake cones, alternating cones and related constructions

Katsuya Eda, Umed H. Karimov, Dušan Repovš, Andreas Zastrow

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

2 Citations (Scopus)

Abstract

We show that the Snake on a square SC(S¹) is homotopy equivalent to the space AC(S¹) which was investigated in the previous work by Eda, Karimov and Repovš. We also introduce related constructions CSC(-) and CAC(-) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.

Original language	English
Pages (from-to)	115-135
Number of pages	21
Journal	Glasnik Matematicki
Volume	48
Issue number	1
DOIs	https://doi.org/10.3336/gm.48.1.11
Publication status	Published - 2013

Keywords

Asphericity
Collapsed alternating cone
Collapsed snake cone
Hawaiian earring
Hawaiian tori
Noncontractible compactum
Peano continuum
Snake on a square
Topologist sine curve
Trivial shape
Weak homotopy equivalence

ASJC Scopus subject areas

Mathematics(all)

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10.3336/gm.48.1.11

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abstract = "We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repov{\v s}. We also introduce related constructions CSC(-) and CAC(-) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.",

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

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language = "English",

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AU - Eda, Katsuya

AU - Karimov, Umed H.

AU - Repovš, Dušan

AU - Zastrow, Andreas

PY - 2013

Y1 - 2013

N2 - We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repovš. We also introduce related constructions CSC(-) and CAC(-) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.

AB - We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repovš. We also introduce related constructions CSC(-) and CAC(-) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.

KW - Asphericity

KW - Collapsed alternating cone

KW - Collapsed snake cone

KW - Hawaiian earring

KW - Hawaiian tori

KW - Noncontractible compactum

KW - Peano continuum

KW - Snake on a square

KW - Topologist sine curve

KW - Trivial shape

KW - Weak homotopy equivalence

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JF - Glasnik Matematicki

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On snake cones, alternating cones and related constructions

Abstract

Keywords

ASJC Scopus subject areas

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