27 citations · 139 across the 20 of their papers we have counts for
16 papers · 1 filter
Twisting of properads
Sergei Merkulov
We study Thomas Willwacher's twisting endofunctor tw in the category of dg properads P under the operad of (strongly homotopy) Lie algebras. It is proven that if P is a properad un…
Quantizations of Lie bialgebras, duality involution and oriented graph complexes
Sergei Merkulov, Marko Živković
We prove that the action of the Grothendieck-Teichmüller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the…
On deformation quantization of quadratic Poisson structures
Anton Khoroshkin, Sergei Merkulov
We study the deformation complex of the dg wheeled properad of -graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich grap…
From deformation theory of wheeled props to classification of Kontsevich formality maps
Assar Andersson, Sergei Merkulov
We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teic…
Grothendieck-Teichmueller group, operads and graph complexes: a survey
Sergei Merkulov
This paper attempts to provide a more or less self-contained introduction into theory of the Grothendieck-Teichmueller group and Drinfeld associators using the theory of operads an…
Prop of ribbon hypergraphs and strongly homotopy involutive Lie bialgebras
Sergei Merkulov
For any integer we introduce a prop of oriented ribbon hypergraphs (in which "edges" can connect more than two vertices) and prove that it admits a canonical morphism…
Multi-oriented props and homotopy algebras with branes
Sergei Merkulov
We introduce a new category of differential graded multi-oriented props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a…
An explicit two step quantization of Poisson structures and Lie bialgebras
Sergei Merkulov, Thomas Willwacher
We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie…
Classification of universal formality maps for quantizations of Lie bialgebras
Sergei Merkulov, Thomas Willwacher
We settle several questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. An importan…
Deformation theory of Lie bialgebra properads
Sergei Merkulov, Thomas Willwacher
We compute the homotopy derivations of the properads governing even and odd Lie bialgebras as well as involutive Lie bialgebras. The answer may be expressed in terms of the Kontsev…
On quantizable odd Lie bialgebras
Anton Khoroshkin, Sergei Merkulov, Thomas Willwacher
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The ma…
Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves
Sergei Merkulov, Thomas Willwacher
We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves (which, according to Penner, i…
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…
Grothendieck-Teichmüller and Batalin-Vilkovisky
Sergei Merkulov, Thomas Willwacher
It is proven that, for any affine supermanifold equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichmüller…
Operads, configuration spaces and quantization
S. A. Merkulov
We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexe…
PROP profile of deformation quantization and graph complexes with loops and wheels
S. A. Merkulov
Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels. We develop some technique for computing cohomol…