Multisimplicial chains and configuration spaces

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.

Major changes after added author