A canonical enriched Adams-Hilton model for simplicial sets
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2004
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| _version_ | 1866909310875860992 |
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| 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 |