Formality of the little N-disks operad

Details Formality of the little N-disks operad Formality of the little N-disks operad

2008-08-04

arxiv.org/abs/0808.0457v2

Mathematics

Algebraic Topology

Exposition improved; gaps filled; 101 pages; submitted for publication

Scientific paper

We develop the details of Kontsevich's proof of the formality of little N-disks operad over the field of real numbers. Formality holds in the category of operads of chain complexes and also in some sense in the category of commutative differential graded algebras, which is the category encoding "real" homotopy theory. We also prove a relative version of the formality for the inclusion of the little m-disks operad in the little N-disks operad for N>=2m+1.

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