2002/04/27 by Clemens Berger, Benoit Fresse
Mathematics · #math.AT #msc:55U10 #msc:18C10
published as C. R. Acad. Sci. Paris Ser. I Math. 335 (2002), pp. 365-370 · Projet de note aux C.R.Acad.Sci.Paris
arxiv created 2002/04/27 · arxiv updated 2009/11/30
The Barratt-Eccles operad is a simplicial operad formed by the classical homogeneous bar construction of the 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).