## JOURNAL OF PURE AND APPLIED ALGEBRA Comparison of the geometric bar and W-constructions (1995)

### BibTeX

@MISC{Berger95journalof,

author = {Clemens Berger and Johannes Huebschmann},

title = {JOURNAL OF PURE AND APPLIED ALGEBRA Comparison of the geometric bar and W-constructions},

year = {1995}

}

### OpenURL

### Abstract

Dedicated to the memory of V.K.A.M. Gugenheim For a simplicial group K, the realization of the W-construction WK + WK of K is shown to be naturally homeomorphic to the universal bundle E]K]--t BIK of its geometric realization]Kl. 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. @ 1998 Elsevier Science B.V. All rights reserved. AMS Cluss$ccrrior~: 55405; 55P35; I8G30

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