Operadic Twisting -- with an application to Deligne's conjecture
By Vasily A. Dolgushev, Thomas Willwacher. 2012
75 citations recorded by the source corpus.
We study categorial properties of the operadic twisting functor Tw. In particular, we show that Tw is a comonad. Coalgebras of this comonad are operads for which a natural notion of twisting by Maurer-Cartan elements exists. We give a large class of examples, including the classical cases of the Lie, associative and Gerstenhaber operads, and their infinity-counterparts L-infinity, A-infinity, G-infinity. We also show that Tw is well behaved with respect to the homotopy theory of operads. As an application we show that every solution of Deligne's conjecture is homotopic to a solution that is compatible with twisting.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/30f85ba0663264f206edf97f05dcbc9d6fd5eec7
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra (2010, methodology): “. A typical graph from fGraphsn(3) (left) and one from Graphsn(4) ⊂ fGraphsn(4) (right). an arrow Lie{k}→TwP. The general theory of operadic twisting is described in Appendix I, and in more detail in [15]. If we apply the twisting functor to the operad Gran (with k= n−1) we obtain an operad fGraphsn”
- The Oriented Graph Complexes (2013, background): “lly an important fact is that there is an action of fcGCor n on fcGraphs or n by operadic derivations. It is constructed as follows. First note that by generalities on operadic twisting (cf. [17] and [4]) one has an action of dfcGC non dfcGraphs . This action cannot create directed cycles in graphs ”