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

Abstract

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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.

How to cite

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Günther, 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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  1. [1] A. Dold und R. Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958), 239-281. 
  2. [2] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Ergeb. Math. Grenzgeb. 35, Springer, 1967. Zbl0186.56802
  3. [3] K. Lamotke, Semisimpliziale algebraische Topologie, Grundlehren Math. Wiss. 147, Springer, 1968. 
  4. [4] J. D. Lawson, Comparison of taut cohomologies, Aequationes Math. 9 (1973), 201-209. Zbl0272.55015
  5. [5] J. P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press, Midway Reprint, 1982. 
  6. [6] L. Mdzinarishvili, Partially continuous Alexander-Spanier cohomology theory, Grüne Preprintreihe der Universität Heidelberg, Heft 130, 1996. 
  7. [7] E. Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163-171. Zbl0055.16203

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