# Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

Bernd Günther; L. Mdzinarishvili

Fundamenta Mathematicae (1997)

- Volume: 153, Issue: 2, page 154-156
- ISSN: 0016-2736

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topGünther, Bernd, and Mdzinarishvili, L.. "Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group." Fundamenta Mathematicae 153.2 (1997): 154-156. <http://eudml.org/doc/212219>.

@article{Günther1997,

abstract = {We prove that Alexander-Spanier cohomology $H^n(X;G)$ with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.
},

author = {Günther, Bernd, Mdzinarishvili, L.},

journal = {Fundamenta Mathematicae},

keywords = {classification of principal bundles; continuous Alexander-Spanier cohomology},

language = {eng},

number = {2},

pages = {154-156},

title = {Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group},

url = {http://eudml.org/doc/212219},

volume = {153},

year = {1997},

}

TY - JOUR

AU - Günther, Bernd

AU - Mdzinarishvili, L.

TI - Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

JO - Fundamenta Mathematicae

PY - 1997

VL - 153

IS - 2

SP - 154

EP - 156

AB - We prove that Alexander-Spanier cohomology $H^n(X;G)$ with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.

LA - eng

KW - classification of principal bundles; continuous Alexander-Spanier cohomology

UR - http://eudml.org/doc/212219

ER -

## References

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- [2] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Ergeb. Math. Grenzgeb. 35, Springer, 1967. Zbl0186.56802
- [3] K. Lamotke, Semisimpliziale algebraische Topologie, Grundlehren Math. Wiss. 147, Springer, 1968.
- [4] J. D. Lawson, Comparison of taut cohomologies, Aequationes Math. 9 (1973), 201-209. Zbl0272.55015
- [5] J. P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press, Midway Reprint, 1982.
- [6] L. Mdzinarishvili, Partially continuous Alexander-Spanier cohomology theory, Grüne Preprintreihe der Universität Heidelberg, Heft 130, 1996.
- [7] E. Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163-171. Zbl0055.16203

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