Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668007 | Advances in Mathematics | 2006 | 29 Pages |
Abstract
For any 1-reduced simplicial set K we define a canonical, coassociative coproduct on ΩC(K), the cobar construction applied to the normalized, integral chains on K, such that any canonical quasi-isomorphism of chain algebras from ΩC(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 [K. Hess, P.-E. Parent, J. Scott, Bimodules over operads characterize morphisms, preprint, math.AT/0505559, 2005].
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