We define an \(E_\infty \)-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of \(E_\infty \)-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.
Medina-Mardones, A., Pizzi, A., Salvatore, P. (2024). Multisimplicial chains and configuration spaces. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 19(2), 275-296 [10.1007/s40062-024-00344-7].
Multisimplicial chains and configuration spaces
Andrea Pizzi;Paolo Salvatore
2024-05-09
Abstract
We define an \(E_\infty \)-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of \(E_\infty \)-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.File in questo prodotto:
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