Operadic Twisting -- with an application to Deligne's conjecture
Abstract
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.
Keywords
Cite
@article{arxiv.1207.2180,
title = {Operadic Twisting -- with an application to Deligne's conjecture},
author = {Vasily Dolgushev and Thomas Willwacher},
journal= {arXiv preprint arXiv:1207.2180},
year = {2014}
}
Comments
To the memory of Jean-Louis Loday. This is yet another revision. Appendix F was completely removed. A separate note will be devoted to this part of the original submission. The final version of this paper will appear in the J. of Pure and Applied Algebra