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arXiv · 1810.02941

The twisting procedure

Vladimir Dotsenko·Sergey Shadrin·Bruno Vallette
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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 à la Willwacher and we perform new homology computations of graph complexes.

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Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette. 2019-02-28. The twisting procedure. https://arxiv.org/abs/1810.02941

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