The Lambrechts-Stanley Model of Configuration Spaces
arXiv:1608.08054 · doi:10.1007/s00222-018-0842-9
Abstract
We prove the validity over 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 , 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.
arXiv comment61 pages. To appear in Inventiones Mathematicae
References in corpus (14)
- Operads and Motives in Deformation Quantization
- Embeddings from the point of view of immersion theory: Part II
- Factorization homology of topological manifolds
- M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
- Remarks on Chern-Simons invariants
- Higher enveloping algebras
- The Homotopy Braces Formality Morphism
- Formality of the chain operad of framed little disks
- Context-free manifold calculus and the Fulton-MacPherson Operad
- Betti numbers and stability for configuration spaces via factorization homology
- Real Homotopy Theory of Semi-Algebraic Sets
- A remarkable DG-module model for configuration spaces
- Rational model of the configuration space of two points in a simply connected closed manifold
- Non-formality of the odd dimensional framed little balls operads