Related papers: Simultaneous deformations and Poisson geometry
We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the…
The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie…
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
We describe the differential graded Lie algebras governing Poisson deformations of a holomorphic Poisson manifold and coisotropic embedded deformations of a coisotropic holomorphic submanifold. In both cases, under some mild additional…
We study deformation of Courant pairs with a commutative algebra base. We consider the deformation cohomology bi-complex and describe a universal infinitesimal deformation. In a sequel, we formulate an extension of a given deformation of a…
We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…
Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…
We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its…
Poisson algebraic structures on current manifolds (of maps from a finite dimensional Riemannian manifold into a 2-dimensional manifold) are investigated in terms of symplectic geometry. It is shown that there is a one to one correspondence…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the $L_\infty$-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we…
We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_\infty$-algebra, which we…
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…
We give an $L_\infty$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again the explicit formulas for all the formal…
Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
We discuss a new class of strong homotopy algebras constructed via inner deformations. Such deformations have a number of remarkable properties. In the simplest case, every one-parameter family of associative algebras leads to an…
Let $P$ be a Poisson structure on a finite-dimensional affine real manifold. Can $P$ be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach -- with respect to all affine Poisson…
In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…