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arXiv · 2012.02060

Multisimplicial chains and configuration spaces

Anibal M. Medina-Mardones·Andrea Pizzi·Paolo Salvatore
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Abstract

This paper presents a generalization to multisimplicial sets of previously defined $E_\infty$-coalgebra structures on the chains of simplicial and cubical sets. We focus on the surjection chain complexes of McClure--Smith as a main example and construct a zig-zag of complexity preserving quasi-isomorphisms of $E_\infty$-coalgebras relating these to both the singular chains on configuration spaces and the Barratt--Eccles chain complexes.

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Anibal M. Medina-Mardones, Andrea Pizzi, Paolo Salvatore. 2020-12-03. Multisimplicial chains and configuration spaces. https://arxiv.org/abs/2012.02060

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