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The Lambrechts-Stanley model of Configuration Spaces

Posted in
Speaker: 
Najib Idrissi
Affiliation: 
Université Lille 1
Date: 
Wed, 2017-02-15 11:00 - 11:30
Location: 
MPIM Lecture Hall

We prove the validity over $R$ of a CDGA model of configuration spaces for
simply connected manifolds of dimension at least $4$, answering a conjecture of
Lambrechts--Stanley.
We get as a result that the real homotopy type of such configuration spaces only depends
on a Poincaré duality model of the manifold.
We moreover prove that our model is compatible with the action of the Fulton--MacPherson operad
when the manifold is framed, by relying on Kontsevich's proof of the formality of the little disks
operads.
We use this more precise result to get a complex computing factorization homology of
framed manifolds.
 

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