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.
Cite
@article{arxiv.1810.02941,
title = {The twisting procedure},
author = {Vladimir Dotsenko and Sergey Shadrin and Bruno Vallette},
journal= {arXiv preprint arXiv:1810.02941},
year = {2019}
}
Comments
New format (short monography), 93 pages, minor corrections, submitted version