A canonical enriched Adams-Hilton model for simplicial sets

Fuente: arXiv
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Hauptverfasser: Hess, Kathryn, Parent, Paul-Eugène, Scott, Jonathan, Tonks, Andrew
Format: Preprint
Veröffentlicht: 2004
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_version_ 1866909310875860992
author Hess, Kathryn
Parent, Paul-Eugène
Scott, Jonathan
Tonks, Andrew
author_facet Hess, Kathryn
Parent, Paul-Eugène
Scott, Jonathan
Tonks, Andrew
contents For any 1-reduced simplicial set $K$ we define a canonical, coassociative coproduct on $\Om C(K)$, the cobar construction applied to the normalized, integral chains on $K$, such that any canonical quasi-isomorphism of chain algebras from $\Om C(K)$ to the normalized, integral chains on $GK$, the loop group of $K$, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the category of chain coalgebras and of strongly homotopy coalgebra maps given in math.AT/0505559.
format Preprint
id arxiv_https___arxiv_org_abs_math_0408216
institution arXiv
publishDate 2004
record_format arxiv
spellingShingle A canonical enriched Adams-Hilton model for simplicial sets
Hess, Kathryn
Parent, Paul-Eugène
Scott, Jonathan
Tonks, Andrew
Algebraic Topology
55P35 (Primary), 16W30, 18D50, 18G35, 55U10, 55U35, 57T05, 57T30 (Secondary)
For any 1-reduced simplicial set $K$ we define a canonical, coassociative coproduct on $\Om C(K)$, the cobar construction applied to the normalized, integral chains on $K$, such that any canonical quasi-isomorphism of chain algebras from $\Om C(K)$ to the normalized, integral chains on $GK$, the loop group of $K$, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the category of chain coalgebras and of strongly homotopy coalgebra maps given in math.AT/0505559.
title A canonical enriched Adams-Hilton model for simplicial sets
topic Algebraic Topology
55P35 (Primary), 16W30, 18D50, 18G35, 55U10, 55U35, 57T05, 57T30 (Secondary)
url https://arxiv.org/abs/math/0408216