131 citations · 651 across the 67 of their papers we have counts for
9 papers · 1 filter
Operadic Torsors
Ricardo Campos, Thomas Willwacher
We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomor…
Differentials on graph complexes
Anton Khoroshkin, Thomas Willwacher, Marko Živković
We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains t…
A Direct Computation of the Cohomology of the Braces Operad
Vasily A. Dolgushev, Thomas H. Willwacher
We give a self-contained and purely combinatorial proof of the well known fact that the cohomology of the braces operad is the operad governing Gerstenhaber algebras…
Representation Homology, Lie Algebra Cohomology and Derived Harish-Chandra Homomorphism
Yuri Berest, Giovanni Felder, Sasha Patotski +2
We study the derived representation scheme DRep_n(A) parametrizing the n-dimensional representations of an associative algebra A over a field of characteristic zero. We show that t…
Relative (non-)formality of the little cubes operads and the algebraic Cerf Lemma
Victor Tourtchine, Thomas Willwacher
It is shown that the operad maps are formal over the reals for and non-formal for . Furthermore we compute the cohomology of the deformation complex…
P. Etingof's conjecture about Drinfeld associators
Carlo A. Rossi, Thomas Willwacher
We construct a family of Drinfeld associators interpolating between the Knizhnik-Zamolodchikov associator, the Alekseev-Torossian associator and the anti-Knizhnik-Zamolodchikov ass…
The Frobenius properad is Koszul
Ricardo Campos, Sergei Merkulov, Thomas Willwacher
We show Koszulness of the prop governing involutive Lie bialgebras and also of the props governing non-unital and unital-counital Frobenius algebras, solving a long-standing proble…
Logarithms and deformation quantization
Anton Alekseev, Carlo A. Rossi, Charles Torossian +1
We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism. This question was open since 1999, and the main obstacle was the presence…
The dimensions and Euler characteristics of M. Kontsevich's graph complexes
Thomas Willwacher, Marko Živković
We provide a generating function for the (graded) dimensions of M. Kontsevich's graph complexes of ordinary graphs. This generating function can be used to compute the Euler charac…