# On the homology of the Harmonic Archipelago

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 863-872
- ISSN: 2391-5455

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topUmed Karimov, and Dušan Repovš. "On the homology of the Harmonic Archipelago." Open Mathematics 10.3 (2012): 863-872. <http://eudml.org/doc/269484>.

@article{UmedKarimov2012,

abstract = {We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.},

author = {Umed Karimov, Dušan Repovš},

journal = {Open Mathematics},

keywords = {Griffiths space; Harmonic Archipelago; Hawaiian Earring; Fundamental group; Trivial shape; Peano continuum; Wild topology; fundamental group; trivial shape; wild topology},

language = {eng},

number = {3},

pages = {863-872},

title = {On the homology of the Harmonic Archipelago},

url = {http://eudml.org/doc/269484},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Umed Karimov

AU - Dušan Repovš

TI - On the homology of the Harmonic Archipelago

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 863

EP - 872

AB - We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.

LA - eng

KW - Griffiths space; Harmonic Archipelago; Hawaiian Earring; Fundamental group; Trivial shape; Peano continuum; Wild topology; fundamental group; trivial shape; wild topology

UR - http://eudml.org/doc/269484

ER -

## References

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- [10] Hatcher A., Algebraic Topology, Cambridge University Press, Cambridge, 2002
- [11] Meilstrup M., Archipelago groups, In: Workshop on Topology of Wild Spaces and Fractals, Strobl, July 4–8, 2011, abstract available at http://dmg.tuwien.ac.at/dorfer/wild_topology/abstracts.pdf
- [12] Spanier E.H., Algebraic Topology, McGraw-Hill, New York-Toronto, 1966

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