English

A prismatic decomposition of the Barratt-Eccles operad

Algebraic Topology 2007-05-23 v1

Abstract

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).

Cite

@article{arxiv.math/0204326,
  title  = {A prismatic decomposition of the Barratt-Eccles operad},
  author = {Clemens Berger and Benoit Fresse},
  journal= {arXiv preprint arXiv:math/0204326},
  year   = {2007}
}

Comments

Projet de note aux C.R.Acad.Sci.Paris

R2 v1 2026-07-22T16:44:53.993Z