Related papers: Graph cohomology classes in the Batalin-Vilkovisky…
We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo…
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The…
In his seminal paper "Formality conjecture", M. Kontsevich introduced a graph complex $GC_{1ve}$ closely connected with the problem of constructing a formality quasi-isomorphism for Hochschild cochains. In this paper, we express the…
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical…
We study a certain class of bulk-boundary systems in the Batalin-Vilkovisky (BV) formalism. We construct factorization algebras of observables for such bulk-boundary systems, and show that these factorization algebras have a natural Poisson…
Kontsevich constructed a map between `good' graph cocycles $\gamma$ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz--Poisson cohomology. For the tetrahedral graph…
We construct a natural chain map from the Kontsevich graph complex to the rational singular chain complex of $B\mathrm{Diff}_\partial(D^{2k})$ when the dimension $2k$ is sufficiently large, generalizing Goussarov and Habiro's theories of…
In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology…
Let $X$ be a compact, oriented, second countable pseudomanifold. We show that $HH^\ast_\bullet(\widetilde N^\ast_\bullet(X;\mathbb{Q}))$, the Hochschild cohomology of the blown-up intersection cochain complex of $X$, is well defined and…
We show under what conditions the complex computing general Ext-groups carries the structure of a cyclic operad such that Ext becomes a Batalin-Vilkovisky algebra. This is achieved by transferring cyclic cohomology theories for the dual of…
Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-Tyutin (BRST) formalism have proved invaluable for classifying consistent deformations of gauge theories. In this work we investigate the…
This paper is devoted to the quantization of the second-ilk superparticle using the Batalin-Vilkovisky method. We show the full structure of the master action. By imposing gauge conditions on the gauge fields rather than on coordinates we…
We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological…
Let $M$ be an exact symplectic manifold with $c_1(M)=0$. Denote by $\mathrm{Fuk}(M)$ the Fukaya category of $M$. We show that the dual space of the bar construction of $\mathrm{Fuk}(M)$ has a differential graded noncommutative Poisson…
Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic Cartan geometry (for example, a holomorphic conformal structure or a holomorphic projective connection). These relations can be calculated…
The double cobar construction of a double suspension comes with a Connes-Moscovici structure, that is a homotopy G-algebra (or Gerstenhaber-Voronov algebra) structure together with a particular BV-operator up to a homotopy. We show that the…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In…
For almost any compact connected Lie group $G$ and any field $\mathbb{F}\_p$, we compute the Batalin-Vilkoviskyalgebra $H^{*+\text{dim }G}(LBG;\mathbb{F}\_p)$ on the loop cohomology of the classifying space introduced byChataur and the…
To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type of the CW…
Given a differential graded (dg) symmetric Frobenius algebra $A$ we construct an unbounded complex $\mathcal{D}^{*}(A,A)$, called the Tate-Hochschild complex, which arises as a totalization of a double complex having Hochschild chains as…