Comparison of the geometric bar and W-constructions

For a simplicial group K, the realization of the W-construction WK → W ̄ K of K is shown to be naturally homeomorphic to the universal bundle E¦K¦→ B¦K¦ of its geometric realization ¦K¦. The argument involves certain recursive descriptions of the W-construction and classifying bundle and relies on t...

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Bibliographic Details
Published in:Journal of pure and applied algebra 1998-10, Vol.131 (2), p.109-123
Main Authors: Berger, Clemens, Huebschmann, Johannes
Format: Article
Language:English
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Summary:For a simplicial group K, the realization of the W-construction WK → W ̄ K of K is shown to be naturally homeomorphic to the universal bundle E¦K¦→ B¦K¦ of its geometric realization ¦K¦. The argument involves certain recursive descriptions of the W-construction and classifying bundle and relies on the facts that the realization functor carries an action of a simplicial group to a geometric action of its realization and preserves reduced cones and colimits.
ISSN:0022-4049
1873-1376
DOI:10.1016/S0022-4049(98)00020-6