A prismatic decomposition of the Barratt-Eccles operad

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

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Algebraic Topology, 55U10, 18C10

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http://salesiana.dossiersoluciones.com/handle/123456789/63920

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204326
 http://arxiv.org/abs/math/0204326
 C. R. Acad. Sci. Paris Ser. I Math. 335 (2002), pp. 365-370

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arXiv