9 citations · 31 across the 14 of their papers we have counts for
18 papers
Accessing non-abelian quotients of the Grothendieck-Teichmueller group via elementary tools
Ivan Bortnovskyi, Vasily A. Dolgushev, Borys Holikov +1
Many challenging questions about the Grothendieck-Teichmueller group, , are motivated by the fact that this group receives the injective homomorphism (called the Ihara embeddin…
GT-shadows for the gentle version of the Grothendieck-Teichmueller group
Vasily A. Dolgushev, Jacob J. Guynee
Let be the Artin braid group on 3 strands and be the corresponding pure braid group. In this paper, we construct the groupoid of GT-shadows for a (possibly more…
The Action of GT-Shadows on Child's Drawings
Vasily A. Dolgushev
GT-shadows are tantalizing objects that can be thought of as approximations of elements of the mysterious Grothendieck-Teichmueller group introduced by V. Drinfeld i…
What are GT-shadows?
Vasily A. Dolgushev, Khanh Q. Le, Aidan A. Lorenz
Let (resp. ) be the braid group (resp. the pure braid group) on 4 strands and be the poset whose objects are finite index normal subgroups of th…
The cohomology of the full directed graph complex
Vasily A. Dolgushev, Christopher L. Rogers
In his seminal paper "Formality conjecture", M. Kontsevich introduced a graph complex closely connected with the problem of constructing a formality quasi-isomorphism fo…
Towards deformation quantization over a Z-graded base
Elif Altinay-Ozaslan, Vasily Dolgushev
The goal of this note is to describe a class of formal deformations of a symplectic manifold in the case when the base ring of the deformation problem involves parameters of no…
When can a formality quasi-isomorphism over rationals be constructed recursively?
V. A. Dolgushev, G. E. Schneider
Let be a differential graded (possibly colored) operad defined over rationals. Let us assume that there exists a zig-zag of quasi-isomorphisms connecting to its c…
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…
A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras
Vasily A. Dolgushev, Christopher L. Rogers
In this paper we consider -algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an quasi-isomorphism $U: L \t…
What do homotopy algebras form?
Vasily A. Dolgushev, Alexander E. Hoffnung, Christopher L. Rogers
In paper arXiv:1406.1744, we constructed a symmetric monoidal category whose objects are shifted (and filtered) L-infinity algebras. Here, we fix a cooperad and show…
On an enhancement of the category of shifted L-infinity algebras
Vasily A. Dolgushev, Christopher L. Rogers
We construct a symmetric monoidal category whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "…
Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group
Vasily Dolgushev, Brian Paljug
Recall that Tamarkin's construction arXiv:math/9803025, arXiv:math/0003052 gives us a map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-is…
A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively
Vasily Dolgushev
It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibl…
The deformation complex is a homotopy invariant of a homotopy algebra
Vasily Dolgushev, Thomas Willwacher
To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have…
Notes on Algebraic Operads, Graph Complexes, and Willwacher's Construction
Vasily A. Dolgushev, Christopher L. Rogers
We give a detailed proof of T. Willwacher's theorem arXiv:1009.1654 which links the cohomology of the full graph complex fGC to the cohomology of the deformation complex of the ope…
Exhausting formal quantization procedures
Vasily Dolgushev
In paper arXiv:1109.6031 the author introduced stable formality quasi-isomorphisms and described the set of its homotopy classes. This result can be interpreted as a complete descr…
Stable Formality Quasi-isomorphisms for Hochschild Cochains
Vasily Dolgushev
We consider L-infinity quasi-isomorphisms for Hochschild cochains whose structure maps admit "graphical expansion". We introduce the notion of stable formality quasi-isomorphism wh…
Formality theorem for Hochschild cochains via transfer
Vasily Dolgushev
We construct a 2-colored operad G^+ which, on the one hand, extends the operad G governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad gover…