English

The twisting procedure

Quantum Algebra 2019-03-05 v2 Algebraic Topology Category Theory K-Theory and Homology Rings and Algebras

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.

Keywords

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

R2 v1 2026-06-23T04:30:26.631Z