Multisimplicial chains and configuration spaces

Medina-Mardones, Anibal M.; Pizzi, Andrea; Salvatore, Paolo

doi:10.1007/s40062-024-00344-7

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Journal Article

Multisimplicial chains and configuration spaces

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Medina-Mardones, Anibal M.
Max Planck Institute for Mathematics, Max Planck Society;

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Salvatore, Paolo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2012.02060
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https://doi.org/10.1007/s40062-024-00344-7
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Medina-Mardones-Pizzi-Salvatore_Multisimplicial chains and configuration spaces_2024.pdf
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Citation

Medina-Mardones, A. M., Pizzi, A., & Salvatore, P. (2024). Multisimplicial chains and configuration spaces. Journal of Homotopy and Related Structures, 19(2), 275-296. doi:10.1007/s40062-024-00344-7.

Cite as: https://hdl.handle.net/21.11116/0000-000F-5A23-5

Abstract

We define an E∞ -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∞-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.