The Lambrechts-Stanley model of configuration spaces
成果类型：
Article
署名作者：
Idrissi, Najib
署名单位：
Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-0842-9
发表日期：
2019
页码：
1-68
关键词：
摘要：
We prove the validity over R of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts-Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on the real homotopy type of the manifold. We moreover prove, if the dimension of the manifold is at least 4, that our model is compatible with the action of the Fulton-MacPherson operad (weakly equivalent to the little disks operad) when the manifold is framed. We use this more precise result to get a complex computing factorization homology of framed manifolds. Our proofs use the same ideas as Kontsevich's proof of the formality of the little disks operads.
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