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Operadic twisting – with an application to Deligne's conjecture


Dolgushev, Vasily; Willwacher, Thomas (2015). Operadic twisting – with an application to Deligne's conjecture. Journal of Pure and Applied Algebra, 219(5):1349-1428.

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 Lie$_\infty$, As$_\infty$, Ger$_\infty$. 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.

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 Lie$_\infty$, As$_\infty$, Ger$_\infty$. 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1 May 2015
Deposited On:28 Jan 2016 08:30
Last Modified:27 Jun 2016 00:00
Publisher:Elsevier
ISSN:0022-4049
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.jpaa.2014.06.010

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