On the homology of the Harmonic Archipelago
Open Mathematics (2012)
- Volume: 10, Issue: 3, page 863-872
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
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
top- [1] Balcerzyk S., On factor groups of some subgroups of a complete direct sum of infinite cyclic groups, Bull. Acad. Polon. Sci., 1959, 7, 141–142
- [2] Bogley W.A., Sieradski A.J., Universal path spaces, preprint available at http://people.oregonstate.edu/_bogleyw/research/ups.pdf
- [3] Conner G., Some interesting open problems in low-dimensional wild topology, 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
- [4] Curtis M.L., Fort M.K. Jr., Singular homology of one-dimensional spaces, Ann. of Math., 1959, 69, 309–313 http://dx.doi.org/10.2307/1970184 Zbl0088.38502
- [5] Eda K., The singular homology groups of certain wild spaces (personal note, September 2011)
- [6] Eda K., Kawamura K., The singular homology of the Hawaiian earring, J. London Math. Soc., 2000, 62(1), 305–310 http://dx.doi.org/10.1112/S0024610700001071 Zbl0958.55004
- [7] Fuchs L., Infinite Abelian Groups. I, Pure Appl. Math., 36, Academic Press, New York-London, 1970
- [8] Griffiths H.B., The fundamental group of two spaces with a common point, Q. J. Math., 1954, 5, 175–190 http://dx.doi.org/10.1093/qmath/5.1.175 Zbl0056.16301
- [9] Harlap A.E., Local homology and cohomology, homological dimension, and generalized manifolds, Mat. Sb. (N.S.), 1975, 96(138), 347–373 Zbl0312.55006
- [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
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.