Related papers: Rational BV-algebra in String Topology
We introduce a Lie algebra of initial terms of logarithmic vector fields along a hypersurface singularity. Extending the formal structure theorem in [GS06, Thm. 5.4], we show that the completely reducible part of its linear projection lifts…
We define a cup product on the Hochschild cohomology of an associative conformal algebra $A$, and show the cup product is graded commutative. We define a graded Lie bracket with the degree $-1$ on the Hochschild cohomology $\HH^{\ast}(A)$…
Chas and Sullivan have defined an intersection-type product on the homology of the free loop space LM of an oriented manifold M. In this paper we show how to extend this construction to a topological conformal field theory of degree d. In…
For a fixed closed manifold $P$, we construct a cobordism category of embedded manifolds with a single Baas-Sullivan singularity of type $P$. Our main theorem identifies the homotopy type of the classifying space of this cobordism category…
The question of vanishing of the BV operator on the cohomology of the moduli space of Riemann surfaces is investigated. The BV structure, which comprises a BV operator and an antibracket, is identified, vanishing theorems are proven, and a…
This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…
Formality is a topological property, defined in terms of Sullivan's model for a space. In the simply-connected setting, a space is formal if its rational homotopy type is determined by the rational cohomology ring. In the general setting,…
Let $G$ be a complex connected reductive algebraic group that acts on a smooth complex algebraic variety $X$, and let $E$ be a $G$-equivariant algebraic vector bundle over $X$. A section of $E$ is regular if it is transversal to the zero…
General theory determines the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product…
We describe the construction of Frobenius manifold out of a cyclic (commutative) $BV_\infty$ algebra $(A,\Delta)$ under the assumption of a Hodge-to-de Rham degeneration property and the existence of a compatible homotopy retract of $A$…
It is known that a single mapping defined on one term of a differential graded vector space extends to a strongly homotopy Lie algebra structure on the graded space when that mapping satisfies two conditions. This strongly homotopy Lie…
The Lie algebra generated by supertranslation and superrotation vector fields at null infinity, known as the extended BMS (eBMS) algebra is expected to be a symmetry algebra of the quantum gravity S matrix. However, the algebra of…
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the…
A *Gerstenhaber-Schack (G-S) bialgebra* consists of a graded Hopf algebra $H$ together with multilinear operations $\{\omega^1_3,\omega^2_2,\omega^3_1\}\subset \{Hom^{-1}(H^{\otimes m},H^{\otimes n}): m+n=4\},$ whose sum is the degree $-1$…
We prove that any Bernstein algebra $(A, \omega)$ is isomorphic to a semidirect product $V \ltimes_{(\cdot, \, \Omega)} \, k$ associated to a commutative algebra $(V, \cdot)$ such that $(x^2)^2 = 0$, for all $x\in A$ and an idempotent…
In this paper we construct a graded Lie algebra on the space of cochains on a $\mathbbZ_2$-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial)…
The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring…
A Brill-Noether stack is an algebraic very presentable stack whose homotopy type has two nontrivial homotopy groups. We consider one with a fundamental group --- a reductive algebraic group-scheme S and one higher homotopy group,…
$G_\infty$-structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a $B_\infty$-algebra by an associative algebra. Actions of $B_\infty$-algebras on…
Let X be a simply connected space and k a commutative ring. Goodwillie, Burghelea and Fiedorowiscz proved that the Hochschild cohomology of the singular chains on the pointed loop space HH^{*}S_*(\Omega X) is isomorphic to the free loop…