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Comptes Rendus Mathématique
Volume 335, n° 4
pages 365-370 (2002)
Doi : S1631-073X(02)02489-5
Received : 8 May 2002 ; 
Une décomposition prismatique de l'opérade de Barratt-Eccles
A prismatic decomposition of the Barratt-Eccles operad
 

Clemens Berger , Benoit Fresse
Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 02, France 

Note présentée par Jean-Pierre Serre

Résumé

L'opérade de Barratt-Eccles est une opérade simpliciale formée par les constructions bar homogènes des groupes symétriques. On montre que ces ensembles simpliciaux se décomposent en réunions de prismes indexés par des surjections. On observe que les complexes cellulaires définis par cette structure prismatique s'identifient aux composantes de l'opérade des surjections (l'opérade introduite par J. McClure et J. Smith dans leur travaux sur la conjecture de Deligne). Pour citer cet article : C. Berger, B. Fresse, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 365-370.

The full text of this article is available in PDF format.
Abstract

The Barratt-Eccles operad is a simplicial operad formed by the classical homogeneous bar construction of symmetric groups. We prove that these simplicial sets decompose as unions of prisms indexed by surjections. We observe that the cellular complexes given by this prismatic structure are nothing but the components of the surjection operad (the operad introduced by J. McClure and J. Smith in their work on the Deligne conjecture). To cite this article: C. Berger, B. Fresse, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 365-370.

The full text of this article is available in PDF format.


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