The twisting procedure

Abstract : This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer--Cartan element. On the way, we settle the integration theory of complete pre-Lie algebras in order to describe this twisting procedure in terms of gauge group action. We give a criterion on quadratic operads for the existence of a meaningful twisting procedure of their associated categories of (homotopy) algebras. We also give a new presentation of the twisting procedure for operads \`a la Willwacher and we perform new homology computations of graph complexes.
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Submitted on : Monday, November 25, 2019 - 1:34:59 PM
Last modification on : Wednesday, November 27, 2019 - 1:38:21 AM

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Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette. The twisting procedure. 2019. ⟨hal-02378802⟩



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