Formality of the Little N-Disks Operad
By P. Lambrechts, Ismar Volic. 2008
145 citations recorded by the source corpus.
Introduction Notation, linear orders, weak partitions, and operads CDGA models for operads Real homotopy theory of semi-algebraic sets The Fulton-MacPherson operad The CDGAs of admissible diagrams Cooperad structure on the spaces of (admissible) diagrams Equivalence of the cooperads D and H * (C[ * ]) The Kontsevich configuration space integrals Proofs of the formality theorems Index of notation Bibliography
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f35cf0b41ffb32c16cec1e5f7b80389bc7b20038
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In Discrete Mathematics and Combinatorics
- Thomas Willwacher
- Victor Turchin
- Valerio Melani
- P. Safronov
- G. Arone
- Victor Tourtchine
- Michael Weiss
- Pedro Boavida de Brito
In Geometry and Topology
- Thomas Willwacher
- Victor Turchin
- G. Arone
- Victor Tourtchine
- P. Safronov
- Valerio Melani
- Ismar Volic
- P. Lambrechts
In Mathematical Physics
- Thomas Willwacher
- Victor Turchin
- G. Arone
- Victor Tourtchine
- P. Safronov
- Valerio Melani
- Ismar Volic
- P. Lambrechts
Citations in the corpus
- Real homotopy theory of semi-algebraic sets (2008, unknown): “1 References 48”
- Derived coisotropic structures II: stacks and quantization (2017, methodology): “Dn ∼=PnJ~K compatible with the equivalence BDn/~∼=Pn. The statement for n= 2 was proved by Tamarkin [Ta] using the existence of rational Drinfeld associators, by Kontsevich [Ko] and Lambrechts–Voli´c [LV] for all n≥2 and k⊃R and finally by Fresse–Willwacher [FW] for all n≥2 and all fields kof characte”
- Graph-complexes computing the rational homotopy of high dimensional analogues of spaces of long knots (2011, background): “iscs and n-discs respectively. One can define a natural inclusion i: Bm →Bn induced by the fixed linear inclusion i: Rm →Rn (we are abusing notation by denoting both inclusions by i). It was shown in [22] that the morphism of operads i ∗: CR(Bm) →CR(Bn) is a formal map of operads when n≥2m. This means”
- On the rational homology of high dimensional analogues of spaces of long knots (2011, background): “t; or \weak bi-module". To begin with, it follows from Kontsevich’s formality theorem [15], or more precisely from the \relative" version of the theorem, introduced by Lambrechts and Volic ([17], and see also [6]), that (under the assumption 2m+ 1 n) the map of operads CR(B m) ! CR(B n) 38”
- M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra (2010, unknown): “We nevertheless give a different short sketch of proof for completeness, following the idea of Lambrechts and Volic [16].”
- Equivalence of formalities of the little discs operad (2009, background): “This construction is explained in great detail in [8].”
- The rational homology of spaces of long knots in codimension > 2 (2007, background): “A more detailed proof can be found in [22].”