2018/10/06 by Vladimir Dotsenko, Sergey Shadrin, Dotsenko, Vladimir +3 · 2 citations
Mathematics · #13D10 #16W60 #17B55 #18D50 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.AT #math.CT #math.KT #math.QA #math.RA #msc:13D10 #msc:16W60 #msc:17B55 #msc:18D50
paper · pdf · doi:10.48550/arxiv.1810.02941
New format (short monography), 93 pages, minor corrections, submitted version
openalex publication_date 2018/10/06 · arxiv created 2019/02/28 · arxiv updated 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.